Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#15668438 | C2 | semidirect |
| 2. C2×#19153822 | C2 | semidirect |
| 3. #26041855 | C2 | semidirect |
| 5. #26041526 | C2 | semidirect |
| 6. #26041509 | C2 | semidirect |
| 7. #26041287 | C2 | semidirect |
| 8. #26041283 | C2 | semidirect |
| 9. #427×C181 | C2 | semidirect |
| 18. C2×#15668432 | C22 | semidirect |
| 19. C2×C8×D181 | C22 | semidirect |
| 25. #19153796 | C22 | semidirect |
| 28. #19153739 | C22 | semidirect |
| 33. #107×C181 | C22 | semidirect |
| 34. #106×C181 | C22 | semidirect |
| 62. C2×C8×C181 | D4 | semidirect |
| 120. C181 | #3057 | semidirect |
| 128. #427 | D181 | semidirect |
| 152. #107 | C2×D181 | semidirect |
| 153. #106 | C2×D181 | semidirect |
| 180. C2×C8 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668438 | 2 |
| C2×#19153822 | 2 |
| #26041855 | 2 |
| #26041848 | 2 |
| #26041526 | 2 |
| #26041509 | 2 |
| #26041287 | 2 |
| #26041283 | 2 |
| #427×C181 | 2 |
| #3057 | 181 |