  We consider models with the $U(1)_X$ gauge symmetry, which is spontaneously
broken by dark Higgs mechanism. We discuss patterns of the electroweak phase
transition and detectability of gravitational waves (GWs) when strongly first
order phase transition (1stOPT) occurs. 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. We find that GWs
produced from multi-step PT can be detected at future observations such as LISA
and DECIGO if the dark photon mass is $m_X^{} \gtrsim 25$ GeV with the
$U(1)_X^{}$ gauge coupling being $g_X^{} \gtrsim 0.5$. In addition, we show
that most of the parameter regions can be covered by precision measurements of
various Higgs boson couplings and direct searches for the singlet scalar boson
at future collider experiments. Furthermore, we expect the complementarity of
the detection of GW observations from the strongly 1stOPT, collider bounds and
dark photon searches in the models of the dark gauge symmetry.
