  We study a model based on the dihedral group D4 in which the dark matter is
stabilized by the interplay between a remnant Z2 symmetry, of the same
spontaneously broken non-abelian group, and an auxiliary Z2 introduced to
eliminate unwanted couplings in the scalar potential. In the lepton sector the
model is compatible with normal hierarchy only and predicts a vanishing reactor
mixing angle. Since m1=0, we also have a simple prediction for the effective
mass in terms of the solar angle. There also exists a large portion of the
model parameter space where the upper bounds on lepton flavor violating
processes are not violated. We incorporate quarks in the same scheme finding
that a description of the CKM mixing matrix is possible and that semileptonic K
and D decays mediated by flavour changing neutral currents are under control.
