  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
\textit{hyperelliptic} as the manifolds admitting such an action. We prove that
the sectional 2-rank of a finite group acting on a 3-manifold and containing a
hyperelliptic involution with fixed-point set with two components has sectional
2-rank at most four; this upper bound is sharp. The cases where the
hyperelliptic involution has a fixed-point set with a number of components
different from 2 have been already considered in literature. Our result
completes the analysis and we obtain some general results where the number of
the components of the fixed-point set is not fixed. In particular, we obtain
that a finite group acting on a 3-manifold and containing a hyperelliptic
involution has 2-rank at most four, and four is the best possible upper bound.
  Finally, we restrict to the basic case of simple groups acting on
hyperelliptic 3-manifolds: we use our result about the sectional 2-rank to
prove that a simple group containing a hyperelliptic involution is isomorphic
to $PSL(2,q)$ for some odd prime power $q$, or to one of four other small
simple groups.
