  We describe field-theory T^2/Z_n orbifolds that offer new ways of breaking
SU(N) to lower rank subgroups. We introduce a novel way of embedding the point
group into the gauge group, beyond the usual mapping of torus and root
lattices. For this mechanism to work the torus Wilson lines must carry
nontrivial 't Hooft flux. The rank lowering mechanism proceeds by inner
automorphisms but is not related to continous Wilson lines and does not give
rise to any associated moduli. We give a complete classification of all
possible SU(N) breaking patterns. We also show that the case of general gauge
group can already be understood entirely in terms of the SU(N) case and the
knowledge of standard orbifold constructions with vanishing 't Hooft flux.
