It is not related to the Suzuki groups of Lie type.
The 24-dimensional Leech lattice has a fixed-point-free automorphism of order 3.
This makes the group 6 · Suz · 2 into a maximal subgroup of Conway's group Co0 = 2 · Co1 of automorphisms of the Leech lattice, and shows that it has two complex irreducible representations of dimension 12.
The group 6 · Suz acting on the complex Leech lattice is analogous to the group 2 · Co1 acting on the Leech lattice.
Wilson (1983) found the 17 conjugacy classes of maximal subgroups of Suz as follows: