The Calabi construction for compact flat orbifolds

A fibered orbifold structure on En/Γ corresponds to a space group extension 1→N→Γ→Γ/N→1. We give a condition for the splitting of a space group extension in terms of the structure group action that is strong enough to detect the splitting of all the space group extensions corresponding to the standard Seifert fibrations of a compact, connected, flat 3-orbifold.