  We analyze the orbifolds that can be obtained as quotients of hyperbolic
3-manifolds admitting a Heegaard splitting of genus two by their orientation
preserving isometry groups. The genus two hyperbolic 3-manifolds are exactly
the hyperbolic 2-fold branched coverings of 3-bridge links. If the 3-bridge
link is a knot, we prove that the underlying topological space of the quotient
orbifold is either the 3-sphere or a lens space and we describe the
combinatorial setting of the singular set for each possible isometry group. In
the case of 3-bridge links with two or three components, the situation is more
complicated and we show that the underlying topological space is the 3-sphere,
a lens space or a prism manifold. Finally we present a infinite family of
hyperbolic 3-manifolds that are simultaneously the 2-fold branched covering of
two inequivalent knot, one with bridge number three and the other one with
bridge number strictly greater than three.
