  We provide a fine classification of Gorenstein quotients of three-dimensional
abelian varieties with isolated singularities, up to biholomorphism and
homeomorphism. This refines a result of Oguiso and Sakurai about fibred
Calabi-Yau threefolds of type $\mathrm{III}_0$. Our proof relies on methods of
crystallographic group theory applied to the orbifold fundamental groups of
such quotients.
