Classification of all N ≥ 3 moduli space orbifold geometries at rank 2

We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional N ≥ 3 superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an N = 2 Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic N = 3 theories.