Fleet Investigation Agency
The FIA is the Fleet intelligence arm.
Activities
Most of FIA's activities are devoted to external threats, but it has an internal review department that oversees Fleet activity. In practice, FIA holds do small covert ops, though this is ostensibly not their remit. This can lead them to some overlap with Special Forces, which is the action arm of the covert/special mission organization. A FIA hold might observe and record data about a pirate base (even to the point of infiltrating it for evidence), for instance, so that a SF team might be sent in to destroy it, or to rescue its slaves. But the FIA hold might end up doing the latter if the observation phase goes wrong, and they're authorized to try if the situation goes to pieces.
Departments
Fleet Intelligence
The part of FIA that concerns itself with intelligence gathering and analysis.
Confusingly, they sometimes call themselves 'FI' as well as 'FIA'.
Internal Review
Oversees issues within Fleet, and particularly between services.
Holds
FIA teams are organized into "holds" that remain together until dissolved, usually for the careers of most of the members. Teams are assigned assets (usually a corvette, if they are abroad, or an office/location if on a planet.)
These are FIA groups that have been featured in stories.