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We consider 3-manifolds admitting the action of an involution such that itsspace of orbits is homeomorphic to $S^3.$ Such involutions are called\textit{hyperelliptic} as the manifolds admitting such an action. We prove thatthe sectional 2-rank of a finite group acting on a 3-manifold and containing ahyperelliptic involution with fixed-point set with two components has sectional2-rank at most four; this upper bound is sharp. The cases where thehyperelliptic involution has a fixed-point set with a number of componentsdifferent from 2 have been already considered in literature. Our resultcompletes the analysis and we obtain some general results where the number ofthe components of the fixed-point set is not fixed. In particular, we obtainthat a finite group acting on a 3-manifold and containing a hyperellipticinvolution 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 onhyperelliptic 3-manifolds: we use our result about the sectional 2-rank toprove that a simple group containing a hyperelliptic involution is isomorphicto $PSL(2,q)$ for some odd prime power $q$, or to one of four other smallsimple groups.

2-rank of finite groups acting on hyperelliptic 3-manifolds