A translation surface is obtained by taking plane polygons and gluing their edges by translations.
We ask which subgroups of the Veech group of a primitive translation surface can be realised via a translation covering.
For many primitive surfaces we prove that partition stabilising congruence subgroups are the Veech group of a covering surface.
We also address the coverings via their monodromy groups and present examples of cyclic coverings in short orbits, i.e. with large Veech groups.