On the classification on finite groups acting on homology 3-spheres

In previous work we showed that the only finite nonabelian simple group acting by diffeomorphisms on a homology 3- sphere is the alternating or dodecahedral group A_5. In the present paper, we characterize the finite nonsolvable groups that act on a homology 3-sphere preserving orientation. We find exactly the finite nonsolvable groups that act orthogonally on the 3-sphere, plus two extra families of groups for which we do not know at present if they really can act on a homology 3-sphere.