  We point out that the moduli spaces of all known 3d $\mathcal{N}=$ 8 and
$\mathcal{N}=$ 6 SCFTs, after suitable gaugings of finite symmetry groups, have
the form $\mathbb{C}^{4r}/\Gamma$ where $\Gamma$ is a real or complex
reflection group depending on whether the theory is $\mathcal{N}=$ 8 or
$\mathcal{N}=$ 6, respectively. Real reflection groups are either dihedral
groups, Weyl groups, or two sporadic cases $H_{3,4}$. Since the BLG theories
and the maximally supersymmetric Yang-Mills theories correspond to dihedral and
Weyl groups, it is strongly suggested that there are two yet-to-be-discovered
3d $\mathcal{N}=$ 8 theories for $H_{3,4}$. We also show that all known
$\mathcal{N}=$ 6 theories correspond to complex reflection groups collectively
known as $G(k,x,N)$. Along the way, we demonstrate that two ABJM theories
$(SU(N)_k\times SU(N)_{-k})/\mathbb{Z}_N$ and $(U(N)_k\times
U(N)_{-k})/\mathbb{Z}_k$ are actually equivalent.

High Energy Physics - Theory