Taken geometrically, a sector really is a silly shape for splitting up a thing as large as a galaxy into administrational or navigational sub-units. You can get three or four sectors which make convenient sub-units, but each one would have bazillions (yes, that's a technical term) of stars and be of marginal utility beyond considering the galaxy as a whole. What you really want is cubical sections roughly tens to maybe hundreds of parsecs across, so each one contains a workable number of stars. You could fit about a million to 10 million such sections into a typical galaxy.

This is taking it literally of course. "Sector" has effectively been neutered of its geometrical meaning in science fiction.