Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
540 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10589855 | C2 | semidirect |
| 2. #10589854 | C2 | semidirect |
| 3. C9×#504 | C2 | semidirect |
| 4. #10588589 | C2 | semidirect |
| 5. #10588588 | C2 | semidirect |
| 6. #10588584 | C2 | semidirect |
| 7. C2×#63359 | C2 | semidirect |
| 15. #63467 | C22 | semidirect |
| 17. C2×Dic36 | C22 | semidirect |
| 18. C9×M32 | C22 | semidirect |
| 19. C2×C9×C16 | C22 | semidirect |
| 20. Dic72 | C22 | semidirect |
| 21. #63359 | C22 | semidirect |
| 22. #63359 | C22 | semidirect |
| 23. #63359 | C22 | semidirect |
| 24. D144 | C22 | semidirect |
| 93. #504 | D9 | semidirect |
| 137. M32 | C2×D9 | semidirect |
| 138. C2×C16 | C2×D9 | semidirect |
| 189. C9 | #3416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589855 | 2 |
| #10589854 | 2 |
| C9×#504 | 2 |
| #10588589 | 2 |
| #10588588 | 2 |
| #10588584 | 2 |
| C2×#63359 | 2 |
| #82014 | 3 |