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We analyze the orbifolds that can be obtained as quotients of hyperbolic3-manifolds admitting a Heegaard splitting of genus two by their orientationpreserving isometry groups. The genus two hyperbolic 3-manifolds are exactlythe hyperbolic 2-fold branched coverings of 3-bridge links. If the 3-bridgelink is a knot, we prove that the underlying topological space of the quotientorbifold is either the 3-sphere or a lens space and we describe thecombinatorial setting of the singular set for each possible isometry group. Inthe case of 3-bridge links with two or three components, the situation is morecomplicated 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 ofhyperbolic 3-manifolds that are simultaneously the 2-fold branched covering oftwo inequivalent knot, one with bridge number three and the other one withbridge number strictly greater than three.

On quotient orbifolds of hyperbolic 3-manifolds of genus two