  We discuss a strongly-coupled extended Higgs sector with the 126 GeV Higgs
boson, which is a low-energy effective theory of the supersymmetric SU(2)$_H$
gauge thoery that causes confinement. In this effective theory, we study the
parameter region where electroweak phase transition is of strongly first order,
as required for successful electroweak baryogenesis. In such a parameter
region, the model has a Landau pole at the order of 10 TeV, which corresponds
to the confinement scale of the SU(2)$_H$ gauge theory. We find that the large
coupling constant which blows up at the Landau pole results in large
non-decoupling loop effects on low-energy observables, such as the
Higgs-photon-photon vertex and the triple Higgs boson vertex. As
phenomenological consequences of electroweak baryogenesis in our model, the
Higgs-to-diphoton branching ratio is about 20% smaller while the triple Higgs
boson coupling is more than about 20% larger than the standard model
predictions. Such deviations may be detectable in future collider experiments.
