Interestingly enough, the actual insignia seemed to have pips below the triangle, which looks more like a sort of mesh. Admiral Aaron had
two pips in "Conspiracy" while Savar had
one, and
Quinn and Admiral
Jameson from "Two Short a Season" had no pips and just the triangle. One could infer that this is the lowest admiral rank since they were both consistently referred to as such, or it's also been speculated that this insignia could have been an early TNG equivalent of a commodore (assuming that Aaron and Savar's insignia follows the later TNG scheme, in which case Aaron would be a two-star rear admiral).
FASA's TNG supplement altered the description of the insignia a bit, likely because the orientation of the pips wasn't clearly visible on screen. Their version actually has a triangular patch with pips inside it, with six pips representing a senior flag/full admiral and five pips a rear admiral. According to FASA, the distinction between these grades was that a rear admiral would command a specific sector or jurisdiction, or even oversee a specific department such as intelligence or ship construction, while a higher admiral would be a staff officer in HQ or administration.
FASA also created the rank of branch admiral, for specialists such as the Starfleet Surgeon General. This rank was below rear admiral and had its own unique insignia, a white shoulder board with a color-coded triangle surrounded by silver oak leaves. Department colors included silver (Inspector General), green (medical), gold (security), and red (engineering).
Edit: Checked Memory Alpha, which confirms that Quinn and Jameson were essentially "lower half" rear admirals which would have been commodore equivalents. Savar was an "upper half" rear admiral, and the naval rank was no longer being used then. Notes for the rank pattern suggest that three pips would have been a full admiral, and four pips a fleet admiral.
