  We consider 3-manifolds admitting the action of an involution such that its
space of orbits is homeomorphic to $S^3.$ Such involutions are called
hyperelliptic as the manifolds admitting such an action. We consider finite
groups acting on 3-manifolds and containing hyperelliptic involutions whose
fixed-point set has $r>2$ components. In particular we prove that a simple
group containing such an involution is isomorphic to $PSL(2,q)$ for some odd
prime power $q$, or to one of four other small simple groups.
