  We study orbifolds of ${\cal N} = 4$ U(n) super-Yang-Mills theory given by
discrete subgroups of SU(2) and SU(3). We have reached many interesting
observations that have graph-theoretic interpretations. For the subgroups of
SU(2), we have shown how the matter content agrees with current quiver theories
and have offered a possible explanation. In the case of SU(3) we have
constructed a catalogue of candidates for finite (chiral) ${\cal N}=1$
theories, giving the gauge group and matter content. Finally, we conjecture a
McKay-type correspondence for Gorenstein singularities in dimension 3 with
modular invariants of WZW conformal models. This implies a connection between a
class of finite ${\cal N}=1$ supersymmetric gauge theories in four dimensions
and the classification of affine SU(3) modular invariant partition functions in
two dimensions.
