Starfleet Command maintains a large staff that oversees the fleets operations and departments.
Properly, Starfleet Command refers to the offices of the Commander, Starfleet, their subordinates the Chief of Starfleet Operation and Starfleet Chief of Staff, as well as their individual staffs, but this is often also used as a synecdoche for Starfleet Headquarters as a whole.
Fleet Admiral Kirsten Clancy (Human)
The Commander, Starfleet (often referred to informally as the CinC, or Commander in Chief) reports directly to the President of the United Federation of Planets. They are in direct command of all of Starfleet, through their subordinates: the Starfleet Chief of Staff and the Chief of Starfleet Operations. The CinC is always a Fleet Admiral and is always the senior-most officer in Starfleet during their term of service.
Chief of Starfleet Operations
The Chief of Starfleet Operations is in direct command of the 20 numbered fleets of Starfleet as well as the Starfleet Auxiliary, each led by an Admiral or Fleet Admiral overseeing 10 to 20 Task Forces, each with 2 to 10 Task Groups. The Chief of Starfleet Operations is always a Fleet Admiral.
Starfleet Chief of Staff
The Chief of Staff oversees all of Starfleet’s Department Chiefs, who in turn oversee Directors of Sub-Departments and Directors of Fleet Divisions, which serve as liaisons between the Starfleet departments and the numbered fleets. The Chief of Staff is always a Fleet Admiral.
Starfleet Operations comprises all of the active starbases and starships in Starfleet, along with Starfleet Auxilary. The Chief of Starfleet Operations maintains a large staff at Starfleet Command which handles moving vessels between fleets and disseminating orders through the appropriate fleet admirals.
Fleet Admiral Teylas Ramar, Commander, Fourth Fleet
Numbered Fleets are the primary organizational unit of Starfleet, consisting of 500 to 1,000 ships each. They are further broken down into Task Forces, which are divided into Task Groups. All numbered fleets are commanded by a flag officer with the rank of Vice Admiral to Fleet Admiral, depending on the size and importance of the fleet--it is customary to refer to the commander of a numbered fleet by “Fleet Admiral” regardless of their actual rank, just as it is customary to refer to the commanding officer of a ship by “Captain.” Fleets have their own staff comprised of the directors of the eight departments’ fleet divisions; this staff advises the fleet admiral.
Admiral TBD, Commander, Starfleet Auxiliary
The Starfleet Auxilary is commanded by an Admiral who shares authority over Starfleet’s minor research vessels, cargo transports, tankers, personnel transports, and hospital ships with the individual department chiefs.
Starfleet Joint Chiefs
The heads of the eight departments of Starfleet reporting to the Chief of Staff compromise the Starfleet Joint Chiefs along with the Chief of Starfleet Operations and Chief of Staff, an advisory board to the Commander, Starfleet and the President of the United Federation of Planets.
Starfleet Science is responsible for overseeing scientific research in Starfleet.
Starfleet Engineering is responsible for technological development, shipbuilding, and other construction tasks in Starfleet.
Starfleet Medical is responsible for medical research and the operations of Starfleet's shipboard, starbase, and planetary medical facilities.
Commodore Oh, Chief of Starfleet Security
Starfleet Security is responsible for the physical safety of Starfleet's assets as well as for planetary defense, dignitary protection, and criminal investigations.
Starfleet Tactical Command
Starfleet Tactical Command is responsible for strategic operations, orbital defense, and tactical training.
Starfleet Intelligence is responsible for gathering information about foreign powers and for protecting the Federation's internal data security.
Starfleet Communications is responsible for developing communications technology and for managing the Federation's subspace relay network.
Admiral TBD, Chief of Starfleet Logistics
Starfleet Logistics is responsible for the training and management of personnel, as well as fuel, supplies, and other materiel for the fleet.
First Contact Office
The Director of the First Contact Office (or DFCO) heads the FCO's operations and is a member of the Starfleet Chiefs of Staff (SCS). Unlike the other Chiefs, the Director is not a Starfleet officer as the FCO is organized as a civilian agency outside of the standard chain of command. Much as a ship's Chief Medical Officer may overrule a commanding officer in areas of medical import, the DFCO may do the same to other fleet officers in areas pertaining to First Contact operations, and is only subordinate to the Commander in Chief and Federation President.
Judge-Advocate General's Corps
The Judge Advocate General's Corps is responsible for judicial proceedings within Starfleet. The Starfleet JAG reports directly to the Federation Council.
Inspector General's Corps
The Inspector General's Corps is responsible for ensuring integrity and probity within Starfleet's office. The Starfleet IG reports directly to the Federation Council.