Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
508 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C3⋊((C22⋊C9)⋊C2) |
| commutator, cosocle, hypocenter | C32⋊(C22⋊C9) | C2×C3 |
| Frattini | C32 | C3×C3⋊S4 |
| Fitting | C22×C34 | D3 |
| socle | C22×C33 | C3⋊D3 |
| LCS | G ▷ C32⋊(C22⋊C9) | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C32⋊(C22⋊C9) | C2 | semidirect |
| 4. #10619761 | C3 | direct (N × H) |
| 9. C32×C22⋊C9 | D3 | semidirect |
| 12. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 28. C22×C33 | D9 | semidirect |
| 41. C3×C22⋊C9 | C3×D3 | semidirect |
| 78. C22×C32 | C3×D9 | semidirect |
| 99. C33 | (C22⋊C9)⋊C2 | semidirect |
| 138. C22×C3 | #4181 | semidirect |
| 156. C32 | C3×(C22⋊C9)⋊C2 | semidirect |
| 176. C22 | C3×#4181 | semidirect |
| 182. C3 | #10619761 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C32⋊(C22⋊C9) | 2 |
| C32×#638 | 3 |
| C32×(C22⋊C9)⋊C2 | 3 |
| #10619761 | 3 |
| C3×#4181 | 4 |