Unconventional superconductivity (SC) featuring multifermion orderings has attracted significant attention. However, previous studies have primarily focused on two-dimensional (2D) systems or 3D systems with effective 2D symmetries. Here, we explore the vestigial phases arising from thermal fluctuations of chiral SC in 3D systems governed by the cubic $O_h$ point group. By constructing low-energy effective Hamiltonians via Ginzburg-Landau analysis and conducting Monte Carlo simulations, we systematically analyze the phase fluctuations of chiral orders within the $E_g$ and $T_{2g}/T_{1u}$ irreducible representations (IRRPs). We identify a phase diagram topology distinct from its 2D counterparts, where the multiphase intersection manifests as a tetracritical point rather than the triple point typically found in 2D systems. Our findings reveal that, for both the $E_g$ and $T_{2g}/T_{1u}$ IRRPs, the primary chiral orders melt into a chiral metallic phase within specific parameter regimes. Furthermore, for the $E_g$ IRRP, phase fluctuations induce a charge-$4e$ phase, while for the $T_{2g}$ and $T_{1u}$ IRRPs, they lead to a higher-order charge-$6e$ SC state. Ultimately, our work highlights the role of nontrivial 3D crystalline symmetries in driving exotic vestigial orders.

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• Superconducting fluctuations
• Superconducting order parameter
• Superconductivity
• Strongly correlated systems
• Unconventional superconductors
• Landau-Ginzburg theory
• XY model