Fleet captain

Fleet captain was a Starfleet title given to a senior captain with a different set of responsibilities than a starship captain. This may have been a higher rank than captain or even commodore, although it did not possess a permanent position in the rank hierarchy.

In 2265, after promotion to fleet captain, Christopher Pike passed command of the starship USS Enterprise (NCC-1701) on to Captain James Kirk. In 2266, as a fleet captain, Pike was engaged in a training exercise aboard an antiquated Class J starship. The vessel's baffle plate ruptured and many of the trainees were killed. A number were saved by Pike--at the cost him being rendered a "complete invalid". Despite his catastrophic injuries, Pike remained on the active duty roster as a command-grade officer. 

In the 2260s, Fleet Captain Garth was one of Starfleet's most decorated captains, the hero of the Battle of Axanar. Garth was injured and recovered among the natives of Antos IV, where he learned of the Antosians' bizarre metamorphic biochemistry control. The strain on Garth's system was too much, he was driven insane by learning their abilities. His life was saved, but maddened, he ordered a starship to fire on the planet, the crew mutinied and Fleet Captain Garth was sentenced to treatment at Elba II. 

Background information
The name plate on the door to Pike's room on Starbase 11 reads simply "Captain Christopher Pike," suggesting that the title "Fleet Captain" is an honorary title and not a rank. Nevertheless, Kirk explicitly stated that Enterprise was summoned by "Fleet Captain Pike", whom he had met when Pike "was promoted to fleet captain." While not definitive, Pike was referred to as "fleet captain" only in the teaser of. The phrase "fleet captain" was never uttered in "Part II", nor was Pike addressed by that title in either part of the episode.

Examination of Kirk's sleeve stripe rank, when compared to that of a commodore, suggests that there may be a "missing rank" between captain and commodore comprised of three solid sleeve stripes in comparison to Kirk's two solid with a center hash mark. This insignia has never made an appearance in any canon or licensed material. The Star Fleet Technical Manual depicts the three stripe insignia (incorrectly) as that of commodore. The Star Trek Encyclopedia featured a Star Trek movies-era fleet captain pin, however, there was no on-screen appearance of the pin, and the insignia was not even part of uniform designer Robert Fletcher's detailed rank notes. Besides the Encyclopedia, there is no insignia for this rank in any other Starfleet uniform code devised, and no similar rank exists in the real-world navies Starfleet was based on. This makes it appear this is simply a title accorded a senior captain.

The reference manual Star Trek: The Next Generation Officer's Manual also speaks on the rank of fleet captain, stating that it is a position held by the heads of ship design teams, with three fleet captains throughout all of Starfleet who are in charge of cruiser-, destroyer-, and escort-class ships respectively. The Manual states that the rank is comprised of five gold pips worn on a uniform collar and, oddly enough, is senior to the rank of commodore.