Oh, we could well argue that the varying designs of uniform patches in TOS denote different "action groups", and Decker was in charge of the one with the Knot symbol, Wesley led the Flower group, while Kirk and Tracey were run-of-the-mill skippers from the Arrowhead and Oblong groups, respectively.
Just to round that list out, in TOS canon, there's the Cardioids to which the Antares
belonged, and the Romulan Neutral Zone outposts and Cestus III evidently belonged to the Seashells. Of course, Starbase 11 appears to be a Flower base.
Throwing in ENT canon, the Defiant
belonged to the Truncated Boomerangs.
TAS canon brings in at least one more, showing that the Huron
belonged to the Starfish. The Ariel,
on the other hand, evidently belonged to the Arrowheads. However, it certainly looks like someone from the Pointy Crosses sat on the Council of Elysia.
or I leave anybody out?