Under the Securities Exchange Act of 1934
(Amendment No. 6)*

(Name of Issuer)

(Title of Class of Securities)

(CUSIP Number)

(Name, Address and Telephone Number of Person
Authorized to Receive Notices and Communications)

(Date of Event Which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§ 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g), check the following box: o

* The remainder of this cover page shall be filled out for a reporting person's initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

SCHEDULE 13D/A

*Pursuant to the Investment Company Act of 1940, as amended, voting rights with respect to Units owned by the Reporting Person generally will be exercised by it in accordance with the directions of its stockholders.

2

This Amendment No. 6 amends and supplements the statement on Schedule 13D, filed on May 31, 2011, as amended by Amendment No. 1 thereto, filed on October 3, 2012, Amendment No. 2 thereto filed on December 11, 2012, Amendment No. 3 thereto filed on March 28, 2013, Amendment No. 4 thereto filed on June 28, 2013 and Amendment No. 5 thereto filed on July 18, 2013  (collectively, the “Schedule 13D”), by New Mountain Finance Corporation, a Delaware corporation (the “Reporting Person”)(1) with respect to the common membership units (“Units”), of New Mountain Finance Holdings, L.L.C., a Delaware limited liability company (the “Issuer”).  Capitalized terms used herein but not defined shall have the meanings ascribed thereto in the Schedule 13D.  Except as herein amended or supplemented, all other information in the Schedule 13D is as set forth therein.

Item 3.   Source and Amount of Funds or Other Consideration

Item 3 of the Schedule 13D is hereby amended to add the following:

On October 17, 2013, the Reporting Person completed an underwritten public offering of 3,000,000 shares of its Common Stock at a public offering price of $14.34 per share (the “October 2013 Primary Offering”). As a result, pursuant to the LLC Agreement as described in Item 6, the Reporting Person used the aggregate net proceeds (after deducting underwriting discounts and commissions) from the October 2013 Primary Offering of $43,020,000 to acquire 3,000,000 Units.

On October 17, 2013, the Reporting Person completed an underwritten public offering of 3,000,000 shares of its Common Stock at a public offering price of $14.34 per share (the “October 2013 Resale Offering”) on behalf of New Mountain Finance AIV Holdings Corporation (“AIV Holdings”). In connection with the October 2013 Resale Offering, AIV Holdings tendered 3,000,000 common membership units of the Operating Company held by AIV Holdings to the Reporting Person in exchange for $41,730,000 of net proceeds (after deducting underwriting discounts and commissions) and the Reporting Person issued 3,000,000 shares of its Common Stock directly to the underwriters for the October 2013 Resale Offering.

On October 22, 2013, as a result of the exercise of the 30-day option to purchase up to an additional 900,000 shares of the Reporting Person’s Common Stock granted to the underwriters in connection with the October 2013 Resale Offering, AIV Holdings tendered an additional 900,000 Units held by AIV Holdings to the Reporting Person in exchange for $12,519,000 of net proceeds (after deducting underwriting discounts and commissions) and the Reporting Person issued 900,000 shares of its Common Stock directly to the underwriters for the October 2013 Resale Offering.

Item 5.   Interest in Securities of the Issuer

Items 5(a) and 5(b) of the Schedule 13D are hereby amended and restated in their entirety as follows:

(1)                                 Neither the present filing nor anything contained herein shall be construed as an admission that (i) the Reporting Person constitutes a “person” for any purposes other than Section 13(d) of the Act, (ii) the Reporting Person is, for purposes of Section 13(d) or Section 16 of the Act or otherwise, a member of a group or (iii) the Reporting Person is, for the purposes of Sections 13(d) of the Act, the beneficial owner of any securities other than securities directly owned by such Reporting Person.

3

(a) — (b).  The aggregate percentage of Units reported owned by the Reporting Person is based upon 47,831,859 Units outstanding, which is the total number of Units outstanding as of October 22, 2013.

For the aggregate number of securities of the Issuer beneficially owned, the percentage of the class of securities of the Issuer beneficially owned, the number of securities for which the Reporting Person has the sole power to vote or to direct the vote, the number of securities for which the Reporting Person has the shared power to vote or to direct the vote, the number of securities for which the Reporting Person has the sole power to dispose or to direct the disposition, and the number of securities for which the Reporting Person has the shared power to dispose or to direct the disposition, see the responses to Items 7 through Item 11 and Item 13 on the attached cover page.

Item 5(c) of the Schedule 13D is hereby amended to add the following:

On October 17, 2013, the Reporting Person completed the October 2013 Primary Offering of 3,000,000 shares of its Common Stock at a public offering price of $14.34 per share. As a result, pursuant to the LLC Agreement as described in Item 6, the Operating Company issued 3,000,000 Units to the Reporting Person in exchange for the net proceeds (after deducting underwriting discounts and commissions) from the October 2013 Primary Offering.

On October 17, 2013, the Reporting Person completed the October 2013 Resale Offering of 3,000,000 shares of its Common Stock at a public offering price of $14.34 per share on behalf of AIV Holdings.  In connection with the October 2013 Resale Offering, AIV Holdings tendered 3,000,000 common membership units of the Operating Company held by AIV Holdings to the Reporting Person in exchange for the net proceeds (after deducting underwriting discounts and commissions) and the Reporting Person issued 3,000,000 shares of its Common Stock directly to the underwriters for the October 2013 Resale Offering.

On October 22, 2013, as a result of the exercise of the 30-day option to purchase up to an additional 900,000 shares of the Reporting Person’s Common Stock granted to the underwriters in connection with the October 2013 Resale Offering, AIV Holdings tendered an additional 900,000 Units held by AIV Holdings to the Reporting Person in exchange for the net proceeds (after deducting underwriting discounts and commissions) and the Reporting Person issued 900,000 shares of its Common Stock directly to the underwriters for the October 2013 Resale Offering.

Item 6.   Contracts, Arrangements, Understandings or Relationships with Respect to Securities of the Issuer

Item 6 of the Schedule 13D is hereby amended to add the following:

In connection with the October 2013 Primary Offering and the October 2013 Resale Offering, the Reporting Person, the Operating Company and AIV Holdings, among others, entered into an underwriting agreement, dated October 11, 2013, with certain underwriters (the “October 2013 Underwriting Agreement”). A more detailed summary of the October 2013 Underwriting Agreement is set forth in the Reporting Person’s Prospectus dated October 11, 2013, as filed with the SEC on October 11, 2013. This summary is qualified in its entirety by the

4

terms of the October 2013 Underwriting Agreement, which is set forth as Exhibit 99.8, and is incorporated herein by reference.

Item 7.   Material to be Filed as Exhibits

Item 7 of the Schedule 13D is hereby amended to add the following:

99.8                        Underwriting Agreement, dated October 11, 2013, filed as Exhibit (h)(4) to the Post-Effective Amendment No. 3 to the Reporting Person’s Registration Statement on Form N-2 dated October 15, 2013, and incorporated herein by reference.

5

SIGNATURES

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

Date:  November 1, 2013

6