  We show that the number of conjugacy classes of maximal finite subgroups of a
lattice in a semisimple Lie group is linearly bounded by the covolume of the
lattice. Moreover, for higher rank groups, we show that this number grows
sublinearly with covolume. We obtain similar results for isotropy subgroups in
lattices. Geometrically, this yields volume bounds for the number of strata in
the natural stratification of a finite-volume locally symmetric orbifold.

Group Theory;Differential Geometry