We consider the decays $htogammagamma,gamma Z$ in the context of an extension of the standard model with two inert doublets and an additional $S_3$ symmetry. This model has contributions for these processes through new charged scalar-loops. Comparing
our $htogammagamma$ with the more precise available experimental data we can predict the behaviour of $htogamma Z$ due that they depend on the same parameters, our estimation for this channel is 1.05 times the standard model value, but can be up to 1.16 if consider the $+1sigma$ uncertainty from the $htogammagamma$ data, and down to 0.96 if consider $-1sigma$.
We study a two scalar inert doublet model (IDMS$_3$) which is stabilized by a $S_3$ symmetry. We consider two scenarios: i) two of the scalars in each charged sector are mass degenerated due to a residual $Z_2$ symmetry, ii) there is no mass degenera
cy because of the introduction of soft terms that break the $Z_2$ symmetry. We show that both scenarios provide good dark matter candidates for some range of parameters.
