Minimum manning for a ship is closer to 12.
Helmsman, engineer, and sensors operator times 3 watch sections makes 9. Officer in Charge, cook, and doc makes 12. Add at least 3 more if the USN requires a lookout in addition to sensor watches (they do when subs are surfaced, so...).
I'd also want a 4th watch section standing a fixed watch (say, 18-24), so that the regular 3 get a better break. This would add another 3+lookout(s).
Example: Section 1 starts off standing the 06-12 watch Monday, the next time they're on watch is midnight-6am Tuesday. They'd normally also stand the 18-24 watch Tuesday but section 4 is kicking them so their next watch isn't until 12-18 on Wednesday (30 hours off watch!). Thursday they're back on the 06-12 watch and pattern repeats.