Finite Group DatabasebetaFinite Group Databasebeta| order | 2304 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | A4×#396⋊C3 |
| Fitting, Sylow | C22×#396 ⋊ C32 |
| derived | C22×#95 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | A4×#126⋊C3 |
| commutator, cosocle, hypocenter | C22×#95 | C2×C32 |
| Frattini | C23 | C2×A42 |
| Fitting | C22×#396 | C32 |
| socle | C25 | C2×C3×A4 |
| LCS | G ▷ C22×#95 | |
| UCS | C1 ◁ C2 | |
649 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 649 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
72 conjugacy classes — view the full character table.
| maximal subgroup of | #72222716, A4×#2842⋊C3 |
| maximal normal subgroup of | A4×#2842⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.