-----BEGIN PRIVACY-ENHANCED MESSAGE-----
Proc-Type: 2001,MIC-CLEAR
Originator-Name: webmaster@www.sec.gov
Originator-Key-Asymmetric:
 MFgwCgYEVQgBAQICAf8DSgAwRwJAW2sNKK9AVtBzYZmr6aGjlWyK3XmZv3dTINen
 TWSM7vrzLADbmYQaionwg5sDW3P6oaM5D3tdezXMm7z1T+B+twIDAQAB
MIC-Info: RSA-MD5,RSA,
 DhnDy4W/ZhmUPws/LJ3XOlIBYZHl11TemcMVdErasWT1eXNJdF/aLrF+3VNht/0M
 0wJAnC83ozrNyHtIAChUFg==

<SEC-DOCUMENT>0001140361-09-024184.txt : 20091030
<SEC-HEADER>0001140361-09-024184.hdr.sgml : 20091030
<ACCEPTANCE-DATETIME>20091030172236
ACCESSION NUMBER:		0001140361-09-024184
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20091030
FILED AS OF DATE:		20091030
DATE AS OF CHANGE:		20091030

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			COGENT COMMUNICATIONS GROUP INC
		CENTRAL INDEX KEY:			0001158324
		STANDARD INDUSTRIAL CLASSIFICATION:	SERVICES-PREPACKAGED SOFTWARE [7372]
		IRS NUMBER:				522337274
		FISCAL YEAR END:			1231

	BUSINESS ADDRESS:	
		STREET 1:		1015 31ST STREET
		CITY:			WASHINGTON
		STATE:			DC
		ZIP:			20007
		BUSINESS PHONE:		2022954200

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			BEURY ROBERT N JR
		CENTRAL INDEX KEY:			0001166979

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	001-31227
		FILM NUMBER:		091149036

	MAIL ADDRESS:	
		STREET 1:		1015 31ST NW
		CITY:			WASHINGTON
		STATE:			DC
		ZIP:			20007
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc1.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0303</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2009-10-30</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001158324</issuerCik>
        <issuerName>COGENT COMMUNICATIONS GROUP INC</issuerName>
        <issuerTradingSymbol>CCOI</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001166979</rptOwnerCik>
            <rptOwnerName>BEURY ROBERT N JR</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1015 31ST ST., NW</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WASHINGTON</rptOwnerCity>
            <rptOwnerState>DC</rptOwnerState>
            <rptOwnerZipCode>20007</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>VP &amp; Chief Legal Officer</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>common stock</value>
            </securityTitle>
            <transactionDate>
                <value>2009-10-30</value>
                <footnoteId id="F1"/>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>1000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>10.334</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>61800</value>
                    <footnoteId id="F2"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The sale of shares of common stock reported here was implemented pursuant to Mr. Beury's structured sale plan (10b5-1 plan).</footnote>
        <footnote id="F2">A portion of these securities is not vested.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Robert N. Beury, Jr.</signatureName>
        <signatureDate>2009-10-30</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
-----END PRIVACY-ENHANCED MESSAGE-----