Finite Group DatabasebetaFinite Group Databasebeta| order | 2592 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
| direct product | D3×C3⋊D3×S4 |
| Fitting, socle | C22×C33 ⋊ C22×D3 |
| derived | C33×A4 ⋊ C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33×A4 | C23 |
| Fitting, socle | C22×C33 | C22×D3 |
| LCS | G ▷ C33×A4 | |
| UCS | C1 | |
2168 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 2168 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
90 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C3⋊D3×#1020, #72220866, C3⋊D3×S42, … |
| maximal normal subgroup of | D33×S4 |
| maximal quotient of | D3×C3⋊D3×#1020, #72220866, C3⋊D3×S42, … |
Past the SmallGroups library coverage — no SmallGroups id.