Extensions of semi-local rings sharing the same group of units

Let B be a ring with only finitely many maximal ideals. We classify all the subrings of B that have the same group of units as B; we show that there are only finitely many of them. As an application, we describe all the domains whose divisibility groups are isomorphic to image for some integer ngreater-or-equal, slanted1 and some order image of image.