We study a model based on the dihedral group D _ { 4 } in which the dark matter is stabilized by the interplay between a remnant Z _ { 2 } symmetry , of the same spontaneously broken non-abelian group , and an auxiliary Z _ { 2 } ^ { f } 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 , \theta _ { 13 } = 0 .
Since m _ { \nu _ { 1 } } = 0 , we also have a simple prediction for the effective mass in terms of the solar angle : |m _ { \beta \beta } | = |m _ { \nu _ { 2 } } | \sin ^ { 2 } \theta _ { \odot } \sim 10 ^ { -3 } eV .
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 flavor changing neutral currents are under control .