This paper presents a search for Higgs bosons decaying to four leptons via one or two light exotic gauge bosons $Z_d$, $H\to Z Z_d \to 4\ell$ and $H \to Z_dZ_d \to 4\ell$ ($\ell=e$ or $\mu$). The search is performed using $pp$ collision data corresponding to an integrated luminosity of about 20~\ifb\ at the center-of-mass energy of \sqrt{s}=8~TeV recorded with the ATLAS detector at the Large Hadron Collider. The observed data are well described by the Standard Model prediction. Upper bounds at 95\% confidence level are set on the relative branching ratios $BR(H \to ZZ_d\to 4\ell)$ to $BR(H \to 4\ell)$ for the exotic vector boson masses between 15 and 55~GeV, and $BR(H \to Z_dZ_d \to 4\ell)$ to $BR(H \to ZZ^* \to 4\ell)$ for the exotic vector boson masses between 15 and 60~GeV.

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