Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #26041756 | C2 | semidirect |
| 4. #26041378 | C2 | semidirect |
| 5. #26041366 | C2 | semidirect |
| 6. #26041287 | C2 | semidirect |
| 8. #26041234 | C2 | semidirect |
| 9. #427×C181 | C2 | semidirect |
| 12. C2×#15668438 | C4 | semidirect |
| 17. #19153781 | C22 | semidirect |
| 23. #19153739 | C22 | semidirect |
| 25. #19153726 | C22 | semidirect |
| 26. C8×Dic181 | C22 | semidirect |
| 30. #107×C181 | C22 | semidirect |
| 31. #106×C181 | C22 | semidirect |
| 35. C2×Dic362 | C2×C4 | semidirect |
| 43. #15668438 | C2×C4 | semidirect |
| 44. #15668438 | C2×C4 | semidirect |
| 54. C2×C8×C181 | C2×C4 | semidirect |
| 103. C181 | #2949 | semidirect |
| 110. #427 | D181 | semidirect |
| 130. #107 | C2×D181 | semidirect |
| 131. #106 | C2×D181 | semidirect |
| 152. C2×C8 | C4×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668438 | 2 |
| #26041756 | 2 |
| #26041753 | 2 |
| #26041378 | 2 |
| #26041366 | 2 |
| #26041287 | 2 |
| #26041283 | 2 |
| #26041234 | 2 |
| #427×C181 | 2 |
| #2949 | 181 |