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In [1] it has been shown that the Cabibbo angle theta_C might arise from adihedral flavor symmetry which is broken to different (directions of) subgroupsin the up and the down quark sector. This leads to a prediction of theta_C interms of group theoretical quantities only, i.e. the index n of the dihedralgroup D_n, the index j of the fermion representation 2_j and the preservedsubgroups indicated by m_u and m_d. Here we construct a low energy model whichincorporates this idea. The gauge group is the one of the Standard Model andD_7 x Z_2 ^(aux) serves as flavor symmetry. The additional Z_2 ^(aux) isnecessary in order to maintain two sets of Higgs fields, one which couples onlyto up quarks and another one coupling only to down quarks. We assume that D_7is broken spontaneously at the electroweak scale by vacuum expectation valuesof SU(2)_L doublet Higgs fields. The quark masses and mixing parameters can beaccommodated well. Furthermore, the potential of the Higgs fields is studiednumerically in order to show that the required configuration of the vacuumexpectation values can be achieved. We also comment on more minimalist modelswhich explain the Cabibbo angle in terms of group theoretical quantities, whiletheta_{13}^q and theta_{23}^q vanish at leading order. Finally, we perform adetailed numerical study of the lepton mixing matrix V_{MNS} in which one ofits elements is entirely determined by the group theory of a dihedral symmetry.Thereby, we show that nearly tri-bi-maximal mixing can also be produced by adihedral flavor group with preserved subgroups.

theta_C from the Dihedral Flavor Symmetries D_7 and D_14