Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23×C32 |
| direct product | C3⋊D3×A4⋊S4 |
| Fitting, socle | C24×C32 ⋊ C2×C3⋊D3 |
| derived | C32×A42 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×A42 | C22 |
| Fitting, socle | C24×C32 | C2×C3⋊D3 |
| LCS | G ▷ C32×A42 | |
| UCS | C1 | |
2854 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 2854 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
84 conjugacy classes — view the full character table.
| maximal subgroup of | D32×A4⋊S4, #72222920, #72222979, … |
| maximal normal subgroup of | D32×A4⋊S4, #72222979, C3⋊D3×S42 |
Past the SmallGroups library coverage — no SmallGroups id.