As one might expect of any bureaucracy, there are very many "sections" within the organisation. None of them have the romance of a fascistic supersecret intelligence group, but you know, sòmeone has to pack out the trash and clean the toilets, right?
If we look in the Technical Manual (© 1975 Franz Josef Designs), we find several hierarchical organisational charts for Star Fleet Armed Forces. We find that most of the "sections" --- divisions officially --- are rather mundane: Fleet Operations, Base Operations, Logistics Support, Personnel Division, Security Division, Science Division, Engineering Division, Medical Division, Technology Support, Colonial Operations, Justice Division, Galaxy Exploration, Space Safety Board, General Accounting, Star Fleet Academy, Planetary Relations.
Each of these broad divisions has sub-offices as well. For example, under the Inspector General we find (inter alia) Fleet Security Forces, U.F.P. Court Officers, U.F.P. Penal Forces, Planetary Marshalls, Internal Investigation, Colonial Security, Information Security.
Refs: pp53 & ff of the Tech Manual can be explored in this PDF.