  Based on a data set of $(27.12\pm0.10)\times 10^8$ $\psi(3686)$ events
collected at the BESIII experiment, the absolute branching fractions of the
three dominant $\Omega^-$ decays are measured to be $\mathcal{B}_{\Omega^- \to
\Xi^0 \pi^-} = (25.03\pm0.44\pm0.53)\%$, $\mathcal{B}_{\Omega^- \to \Xi^-
\pi^0} = (8.43\pm0.52\pm0.28)\%$, and $\mathcal{B}_{\Omega^- \to \Lambda K^-} =
(66.3\pm0.8\pm2.0)\%$, where the first and second uncertainties are statistical
and systematic, respectively. The ratio between $\mathcal{B}_{\Omega^- \to
\Xi^0 \pi^-}$ and $\mathcal{B}_{\Omega^- \to \Xi^- \pi^0}$ is determined to be
$2.97\pm0.19\pm0.11$, which is in good agreement with the PDG value of
$2.74\pm0.15$, but greater by more than four standard deviations than the
theoretical prediction of 2 obtained from the $\Delta I = 1/2$ rule.
