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.
