Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C24×C33 |
| direct product | C32×D3×C22⋊A4 |
| Fitting, socle | C24×C33 ⋊ C2×C3 |
| derived | C24×C3 ⋊ C2×C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D3×C22⋊A4 |
| commutator, cosocle, hypocenter | C24×C3 | C2×C33 |
| Frattini | C1 | G |
| Fitting, socle | C24×C33 | C2×C3 |
| LCS | G ▷ C24×C3 | |
| UCS | C1 ◁ C32 | |
2930 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 2930 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
216 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×C22⋊A4, C32×D3×#1020, D3×C3⋊(C3⋊#1020), … |
| maximal normal subgroup of | D3×C3⋊D3×C22⋊A4, C32×D3×#1020, D3×C3⋊(C3⋊#1020), … |
Past the SmallGroups library coverage — no SmallGroups id.