  In early 1930s Seifert and Threlfall classified up to conjugacy the finite
subgroups of $\mathrm{SO}(4)$, this 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 $\mathrm{SO}(4)$ with the invariants of the
corresponding fibered 3-orbifolds. This allows to deduce directly from the
algebraic classification topological properties of spherical 3-orbifolds.
