  We consider a standard model extension equipped with a dark sector where the
$U(1)_X^{}$ Abelian gauge symmetry is spontaneously broken by the dark Higgs
mechanism. In this framework, we investigate patterns of the electroweak phase
transition as well as those of the dark phase transition, and examine
detectability of gravitational waves (GWs) generated by such strongly first
order phase transition. It is pointed out that the collider bounds on the
properties of the discovered Higgs boson exclude a part of parameter space that
could otherwise generate detectable GWs. After imposing various constraints on
this model, it is shown that GWs produced by multi-step phase transitions are
detectable at future space-based interferometers, such as LISA and DECIGO, if
the dark photon is heavier than 25 GeV. Furthermore, we discuss the
complementarity of dark photon searches or dark matter searches with the GW
observations in these models with the dark gauge symmetry.
