A study of long-lived dark Z boson that either couples directly to quarks or mixes kinetically with the standard model Z boson is performed. Production via a vector portal and the Higgs portal are considered. The impact of additionally mixing the standard model Higgs boson with a dark Higgs boson on the production and decays of the dark Z is evaluated. Specifically, decays with a final state of displaced dimuons are considered where the dark Z and the dark Higgs decay directly to a dimuon or indirectly via dark scalars or fermions to an even number of dimuons, which can give rise to final states with large muon multiplicities. The production and total cross sections of the processes of interest as well as decay widths and decay lengths are calculated by applying Monte Carlo simulation using the framework of MadGraph5_aMC@NLO v2.7.0. The sensitivity for such searches in Runs 2 and 3 of the Large Hadron Collider is discussed. Kinematics of the displaced dimuons is also investigated.