Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
741 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 741 conjugacy classes of subgroups — too many to draw. Only its 166 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. #10589918 | C2 | semidirect |
| 2. C22×#3675 | C2 | semidirect |
| 4. #10589623 | C2 | semidirect |
| 5. C9×#419 | C2 | semidirect |
| 6. #10588803 | C2 | semidirect |
| 7. #10588683 | C2 | semidirect |
| 8. #10588499 | C2 | semidirect |
| 9. #10588498 | C2 | semidirect |
| 16. #63509 | C22 | semidirect |
| 18. #63506 | C22 | semidirect |
| 30. C9×#103 | C22 | semidirect |
| 31. Dic9⋊C8 | C22 | semidirect |
| 32. #63369 | C22 | semidirect |
| 33. #63368 | C22 | semidirect |
| 137. #419 | D9 | semidirect |
| 209. #103 | C2×D9 | semidirect |
| 294. C9 | #3042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589918 | 2 |
| C22×#3675 | 2 |
| C2×#63470 | 2 |
| #10589623 | 2 |
| C9×#419 | 2 |
| #10588803 | 2 |
| #10588683 | 2 |
| #10588499 | 2 |
| #10588498 | 2 |
| #78976 | 3 |