Including the various air wings onboard and the division head who could be captains of that billet/position, I believe it is thirteen.
Who told you 13?
For one, there is only ever ONE "Air Wing" on a Carrier.
And two, no "division" would ever be led by a Captain. Department, yes. Division, no.
I think the most 0-6 Captains we ever had onboard at one time (normally assigned personnel doing their normally assigned jobs, no visitors or anything) was maybe
13 is just completely unrealistic.