Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
714 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10589819 |
| commutator, cosocle | C2×C4×C9 | C24 |
| Frattini | C2×C3×C4 | C23×D3 |
| Fitting | C9×#493 | C2 |
| socle | C2×C3 | #5717 |
| hypercenter | #493 | D9 |
| hypocenter | C9 | #3292 |
| LCS | G ▷ C2×C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10589859 | C2 | semidirect |
| 2. C9×#493 | C2 | semidirect |
| 3. #10588840 | C2 | semidirect |
| 4. #10588757 | C2 | semidirect |
| 5. #10588380 | C2 | semidirect |
| 7. #63710 | C22 | semidirect |
| 8. C2×C9×D8 | C22 | semidirect |
| 9. C9×#127 | C22 | semidirect |
| 10. #63495 | C22 | semidirect |
| 15. #63464 | C22 | semidirect |
| 16. C4×C8×C9 | C22 | semidirect |
| 17. #63391 | C22 | semidirect |
| 18. #63372 | C22 | semidirect |
| 19. #63364 | C22 | semidirect |
| 38. D72 | D4 | semidirect |
| 39. #3664 | D4 | semidirect |
| 42. Dic36 | D4 | semidirect |
| 73. #493 | D9 | semidirect |
| 109. C2×D8 | C2×D9 | semidirect |
| 111. #127 | C2×D9 | semidirect |
| 115. C4×C8 | C2×D9 | semidirect |
| 161. C9 | #3292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589859 | 2 |
| C9×#493 | 2 |
| #10588840 | 2 |
| #10588757 | 2 |
| #10588380 | 2 |
| #81791 | 3 |