Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
684 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 214 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D9 |
| commutator | C22×C9 | C23×C4 |
| Frattini, socle | C23×C3 | C23×D3 |
| Fitting | C9×#384 | C2 |
| prime radical | C23×D9 | C23 |
| cosocle | C23×C9 | C24 |
| hypercenter | #384 | D9 |
| hypocenter | C9 | #2383 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C9×#384 | C2 | semidirect |
| 5. #10588658 | C2 | semidirect |
| 6. #10588656 | C2 | semidirect |
| 7. #10588617 | C2 | semidirect |
| 18. #63438 | C4 | semidirect |
| 40. C42×C9 | C2×C4 | semidirect |
| 44. Dic9⋊C4 | C2×C4 | semidirect |
| 84. #384 | D9 | semidirect |
| 165. C42 | C4×D9 | semidirect |
| 178. C9 | #2383 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63438 | 2 |
| C9×#384 | 2 |
| #10588670 | 2 |
| #10588669 | 2 |
| #10588658 | 2 |
| #10588656 | 2 |
| #10588617 | 2 |
| #74361 | 3 |