  We investigate the potential reach of a search for a long-lived/prompt dark
vector boson $Z_D$, also called dark $Z$, and a prompt dark Higgs boson $h_D$
through exotic decays of the observed Higgs boson $h$ into either $Z_DZ_D$,
$h_Dh_D$, or $ZZ_D$ with $Z$ being the hypercharge gauge boson. The $Z_D$
production through the Higgs portal is completed via one of two mechanisms,
kinetic mixing of $Z_D$ with $Z$ and the mixing of $h_D$ with $h$. All
production modes of $h$ are considered, while the branching fractions are
calculated in Monte Carlo simulation using the {\textsc{MadGraph5}}\_aMC@NLO
v2.7.2 framework. We focus on a final state of multiple dimuons, displaced up
to \mbox{7500 mm}, where the muons can be reconstructed without vertex
constraint using data from ATLAS and CMS detectors to be collected in Run~3.
Integrated luminosities of 137, 300, and 3000 fb$^{-1}$ for Run~2, Run~3, and
high luminosity run (HL-LHC), respectively, are used for estimating the
expected search sensitivity of the Large Hadron Collider to each of the decay
modes.
