Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26041831 | C2 | semidirect |
| 3. #26041614 | C2 | semidirect |
| 4. #26041558 | C2 | semidirect |
| 5. #26041483 | C2 | semidirect |
| 8. #26041382 | C2 | semidirect |
| 9. #26041378 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 11. #484×C181 | C2 | semidirect |
| 16. #19153815 | C22 | semidirect |
| 17. #19153814 | C22 | semidirect |
| 21. Q8×Dic181 | C22 | semidirect |
| 23. #19153781 | C22 | semidirect |
| 31. #19153749 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153739 | C22 | semidirect |
| 37. #19153726 | C22 | semidirect |
| 40. #107×C181 | C22 | semidirect |
| 41. #103×C181 | C22 | semidirect |
| 136. C181 | #3110 | semidirect |
| 141. #484 | D181 | semidirect |
| 171. #107 | C2×D181 | semidirect |
| 174. #103 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041831 | 2 |
| C2×#19153778 | 2 |
| #26041614 | 2 |
| #26041558 | 2 |
| #26041483 | 2 |
| #26041432 | 2 |
| #26041429 | 2 |
| #26041382 | 2 |
| #26041378 | 2 |
| #26041333 | 2 |
| #484×C181 | 2 |
| #3110 | 181 |