Light propagation in an inhomogeneous, anisotropic medium is discussed. The medium shows the most general anisotropy (optically biaxial) and a special kind of inhomogeneity: rotation of a principal axis of the dielectric tensor about the z-axis. Since the analytic treatment is very troublesome, we use group theory to deduce qualitative statements on frequency splitting in the Brillouin diagram. As in all periodic anisotropic media, where two different group velocities exist, an infinite number of stop bands is produced by a splitting into maximally three stop bands at each point of interaction. Two special cases for the dielectric tensor are treated also: optically biaxial media with one axis in the z -direction and optically uniaxial media with an oblique optical axis. The group theory required is similar to the theory of crystallographic double space groups.