Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26042093 | C2 | semidirect |
| 2. #26042091 | C2 | semidirect |
| 3. #26042081 | C2 | semidirect |
| 4. #26041663 | C2 | semidirect |
| 5. #26041555 | C2 | semidirect |
| 6. #26041550 | C2 | semidirect |
| 7. #26041542 | C2 | semidirect |
| 8. #26041458 | C2 | semidirect |
| 9. #26041453 | C2 | semidirect |
| 10. #26041397 | C2 | semidirect |
| 11. #443×C181 | C2 | semidirect |
| 12. #19153863 | C22 | semidirect |
| 16. #19153846 | C22 | semidirect |
| 19. #19153844 | C22 | semidirect |
| 26. C2×Dic724 | C22 | semidirect |
| 29. C2×#15668438 | C22 | semidirect |
| 33. #19153822 | C22 | semidirect |
| 34. #19153804 | C22 | semidirect |
| 35. #19153752 | C22 | semidirect |
| 37. #19153744 | C22 | semidirect |
| 38. #19153734 | C22 | semidirect |
| 39. #19153732 | C22 | semidirect |
| 41. #131×C181 | C22 | semidirect |
| 42. #108×C181 | C22 | semidirect |
| 43. #104×C181 | C22 | semidirect |
| 44. C4×C8×C181 | C22 | semidirect |
| 149. C181 | #3290 | semidirect |
| 161. #443 | D181 | semidirect |
| 185. #131 | C2×D181 | semidirect |
| 188. #108 | C2×D181 | semidirect |
| 191. #104 | C2×D181 | semidirect |
| 194. C4×C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042093 | 2 |
| #26042091 | 2 |
| #26042081 | 2 |
| #26041663 | 2 |
| #26041555 | 2 |
| #26041550 | 2 |
| #26041542 | 2 |
| #26041458 | 2 |
| #26041453 | 2 |
| #26041397 | 2 |
| #443×C181 | 2 |
| #3290 | 181 |