Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
676 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #11758088 |
| commutator, Fitting, cosocle | C2×C33×C9 | C22 |
| Frattini | C2×C3 | C3⋊#1113 |
| socle | C2×C34 | C2×D3 |
| hypocenter | C33×C9 | D4 |
| LCS | G ▷ C2×C33×C9 ▷ C33×C9 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C9×C3⋊(C3⋊D3) | C2 | semidirect |
| 2. C2×C32×C3⋊D9 | C2 | semidirect |
| 3. C3×C3⋊(C3⋊Dic9) | C2 | semidirect |
| 16. C2×C3×C3⋊D9 | D3 | semidirect |
| 19. C3⋊(C3⋊Dic9) | D3 | semidirect |
| 22. C33×C9 | D4 | semidirect |
| 43. C2×C3⋊(C3⋊D3) | D9 | semidirect |
| 55. C2×C3⋊D9 | C3⋊D3 | semidirect |
| 70. C32×C9 | D12 | semidirect |
| 71. C32×C9 | #67 | semidirect |
| 133. C33 | #611 | semidirect |
| 143. C3×C9 | #626 | semidirect |
| 144. C3×C9 | #638 | semidirect |
| 198. C32 | #6194 | semidirect |
| 199. C32 | #6195 | semidirect |
| 205. C9 | #6291 | semidirect |
| 229. C3 | #10619877 | semidirect |
| 230. C3 | #10619899 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C3⋊(C3⋊D3) | 2 |
| C2×C32×C3⋊D9 | 2 |
| C3×C3⋊(C3⋊Dic9) | 2 |
| #10620157 | 3 |
| #10619899 | 3 |
| #10619877 | 3 |