On unramified normal coverings of hyperelliptic curves

It is well known that the number of unramified   normal coverings of an irreducible complex algebraic curve CC with a group of covering transformations isomorphic to Z2⊕Z2Z2⊕Z2 is (24g−3⋅22g+2)/6(24g−3⋅22g+2)/6. Assume that CC is hyperelliptic, say C:y2=∏d=12g+2(x−μd). Horiouchi has given the explicit algebraic equations of the subset of those covers which turn out to be hyperelliptic themselves. There are (2g+23) of this particular type. In this article, we provide algebraic equations for the remaining ones.