Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
297 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #63457 |
| commutator, cosocle | C42×C9 | C23 |
| Frattini | C3×C42 | C22×D3 |
| Fitting | C9×#334 | C2 |
| socle | C22×C3 | #895 |
| hypercenter | #334 | D9 |
| hypocenter | C9 | #1687 |
| LCS | G ▷ C42×C9 ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #334 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10588527 | C2 | semidirect |
| 2. #10588377 | C2 | semidirect |
| 3. #10588370 | C2 | semidirect |
| 4. C9×#334 | C2 | semidirect |
| 5. #10588163 | C2 | semidirect |
| 67. C8×C9 | D8 | semidirect |
| 72. #334 | D9 | semidirect |
| 164. C9 | #1687 | semidirect |
| 182. C8 | D72 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588527 | 2 |
| #10588377 | 2 |
| #10588370 | 2 |
| C9×#334 | 2 |
| #10588163 | 2 |
| #68540 | 3 |