  In this paper we study finite semiprimitive permutation groups, that is,
groups in which each normal subgroup is transitive or semiregular. We give
bounds on the order, base size, minimal degree, fixity, and chief length of an
arbitrary finite semiprimitive group in terms of its degree. To establish these
bounds, we classify finite semiprimitive groups that induce the alternating or
symmetric group on the set of orbits of an intransitive normal subgroup.
