  We study cosmological dynamics of a generalized Higgs inflation. By expanding
the action up to the second and third order in the small perturbations, we
study the primordial perturbation and its non-Gaussian distribution. We study
the non-Gaussian feature in both the equilateral and orthogonal configurations.
By adopting a quartic potential, we perform a numerical analysis on the model's
parameter space and compare the results with Planck2015 observational data. To
obtain some observational constraint, we focus on the self-coupling and the
non-minimal coupling parameters. We show that, in the presence of the
non-minimal coupling and the Galileon-like interaction, the self-coupling
parameter can be reduced to the order of $10^{-6}$ which is much larger than
the value that CMB normalization suggests for this self-coupling.
