As far as I can tell there were 6. They were:
1 - The Warren Commission
2 - The Ramsey Clark Report
3 - The Rockefeller Commission
4 - The Church Committee
5 - The HSCA Investigation
6 - The ARRB (yes I know, not really an "investigation", but it kinda was)
There was also the Pike Committee report in the 1970’s. However I’m not sure if that report investigated any part of the JFK assassination. Does anyone know?
There were also other investigations such as:
Texas Supplemental Report on the Assassination of President John F. Kennedy and the Serious Wounding of Governor John B. Connally(LINK:
https://www.maryferrell.org/showDoc.html?docId=20 )
Investigation of The Operational Security Involving The Transfer of Lee Harvey Oswald – November 24, 1963 1963 (LINK:
https://www.baylor.edu/content/services/document.php/75604.pdf )
Kennedy, John Fitzgerald Assassination – Nov. 22, 1963 Investigation By J. E. Bill Decker, Sheriff Dallas County, Texas(LINK:
https://www.baylor.edu/content/services/document.php/75604.pdf )
But these 3 would not be considered government investigations? Perhaps you could call them "official" investigations but not "government" investigations.