Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#19153844 | C2 | semidirect |
| 2. C2×#19153824 | C2 | semidirect |
| 3. #26041860 | C2 | semidirect |
| 4. #26041848 | C2 | semidirect |
| 5. #26041533 | C2 | semidirect |
| 6. #26041526 | C2 | semidirect |
| 7. #26041516 | C2 | semidirect |
| 8. #26041509 | C2 | semidirect |
| 9. #26041273 | C2 | semidirect |
| 10. C2×#19153736 | C2 | semidirect |
| 11. #428×C181 | C2 | semidirect |
| 19. C2×#15668432 | C22 | semidirect |
| 21. C2×C8×D181 | C22 | semidirect |
| 25. #19153796 | C22 | semidirect |
| 29. #19153791 | C22 | semidirect |
| 32. #19153739 | C22 | semidirect |
| 33. #19153739 | C22 | semidirect |
| 36. #19153736 | C22 | semidirect |
| 37. #19153736 | C22 | semidirect |
| 41. #107×C181 | C22 | semidirect |
| 42. #106×C181 | C22 | semidirect |
| 77. M16×C181 | D4 | semidirect |
| 151. C181 | #3062 | semidirect |
| 161. #428 | D181 | semidirect |
| 187. #107 | C2×D181 | semidirect |
| 188. #106 | C2×D181 | semidirect |
| 220. M16 | D724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153844 | 2 |
| C2×#19153824 | 2 |
| #26041860 | 2 |
| #26041848 | 2 |
| #26041533 | 2 |
| #26041526 | 2 |
| #26041516 | 2 |
| #26041509 | 2 |
| #26041273 | 2 |
| C2×#19153736 | 2 |
| #428×C181 | 2 |
| #3062 | 181 |