McCone was a JFK loyalist and kept out of the loop.
Former CIA Director Allen Dulles was fired by JFK and he was one of the key conspirators. Others included counter-intelligence chief Angleton and the Western Hemisphere operations team.
LBJ and J Edgar Hoover were conspirators as well.
For more on LBJ’s role, Roger Stone’s book on the subject is the best:
https://www.amazon.com/Man-Who-Killed-Kennedy-Against/dp/1626363137