Delta Force isn't a part of the CIA. Delta Force is a "special mission unit" ran by JSOC, which is a component of SOCOM that handles Tier One units. SOCOM is the overarching agency that runs all special forces and SMU in the entire US military that answers directly to the President and Secretary of Defense, supposedly. The CIA is completely separate from SOCOM. Their special forces units are the Special Operations Group (SOG) which does boots on the ground military action, and the Political Actions Group (PAG) which conducts psyops, subversion, demoralization, etc. These units comprise the CIA's own internal special forces division called Special Activities Center. The SAC is actually a level deeper than Delta and DEVGRU and other Special Missions Units because they recruit from within JSOC, which are already the highest level one can attain within the US military.