From my understanding, The Gaggi crew was under Greg dePalma after Gaggi.

Originally, it was Paul Castellano's crew so it has been one of a key crews in the Gambino family for a while. Gaggi was Big Paul's protégé and Catsellano made him capo of his crew when he got the top spot.

When Gaggi went to jail / died, John Gotti made Greg dePalma a captain, supposedly as a reward for bringing a major construction company under the control of the Gambinos. At this point, this crew was nothing like the old Gaggi/DeMeo crew. It seems that all the guys from that era have either died or gone to jail so i don't think there was much continuity from the Gaggi crew to the dePalma one.