It is now clear that the masses of the neutrino sector are much lighter than those of the other three sectors.There are many attempts to explain the neutrino masses radiatively by means of inert Higgses, which dont have vacuum expectation values. Then one can discuss cold dark matter candidates, because of no needing so heavy particles and having a $Z_2$ parity symmetry corresponding to the R-parity symmetry of the MSSM. The most famous work would be the Zee model. Recently a new type model along this line of thought was proposed by E. Ma. We introduce a flavor symmetry based on a dihedral group $D_6$ to constrain the Yukawa sector. For the neutrino sector, we find that the maximal mixing of atmospheric neutrinos is realized, it can also be shown that only an inverted mass spectrum, the value of $|V_{MNS_{13}}|$ is 0.0034 and so on. For the fermionic CDM candidates, we find that the mass of the CDM and the inert Higgs should be larger than about 230 and 300 GeV, respectively. If we restrict ourselves to a perturbative regime, they should be lighter than about 750 GeV.
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