In early 1930s, Seifert and Threlfall classified up to conjugacy the finite subgroups of $\SO4$, which gives an algebraic classification of orientable spherical 3-orbifolds.
For the most part, spherical 3-orbifolds are Seifert fibered. The underlying topological space and singular set of non-fibered spherical 3-orbifolds were described by Dunbar. In this paper we deal with the fibered case and in particular we give explicit formulae relating the finite subgroups of $\SO4$ with the invariants of the corresponding fibered 3-orbifolds. This allows us to deduce directly from the algebraic classification topological properties of spherical 3-orbifolds.
