There's seven in total, counting the plaza in the middle — you can access a map over the facility through your communicator, if you need one.
The sectors are vaguely thematic: sector 1 has a warmer climate with a beach, sector 2 is more modern and focused on intellectual pursuits, sector 3 seems to be modeled after what we would know as Asia whereas sector 4 has a more European feel. Sector 5 is, quite fittingly, gothic in its architecture and hosts the hospital and graveyard. I've already mentioned sector 6.
Then there's sector 0 in the middle, connecting the other six. That's where you'll find the warden kiosk.