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A supersymmetric extension of the standard model based on the discrete $Q_6$family symmetry is considered, and we investigate flavor-changing neutralcurrent (FCNC) processes, especially those mediated by heavy flavor-changingneutral Higgs bosons. Because of the family symmetry the number of theindependent Yukawa couplings is smaller than that of the observed quantitiessuch as the Cabibbo-Kobayashi-Maskawa matrix and the quark masses, so that theFCNCs can be parametrized only by the mixing angles and masses of the Higgsfields. We focus our attention on the mass differences of the neutral $K, D$and $B$ mesons. All the constraints including that from the ratio $\DeltaM_{B_s}/\Delta M_{B_d}$ can be satisfied, if the heavy Higgs bosons are heavierthan $\sim 1.5$ TeV. If the constraint from $\Delta M_K$ is slightly relaxed,the heavy Higgs bosons can be as light as $\sim 0.4$ TeV, which is within theaccessible range of LHC.

Flavor Changing Neutral Higgs Bosons in a Supersymmetric Extension based on a $Q_6$ Family Symmetry