Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
448 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26041834 | C2 | semidirect |
| 3. #26041611 | C2 | semidirect |
| 4. #26041566 | C2 | semidirect |
| 5. #26041485 | C2 | semidirect |
| 6. #26041484 | C2 | semidirect |
| 8. #26041370 | C2 | semidirect |
| 9. #26041366 | C2 | semidirect |
| 10. #26041331 | C2 | semidirect |
| 11. #476×C181 | C2 | semidirect |
| 16. #19153816 | C22 | semidirect |
| 21. #19153781 | C22 | semidirect |
| 31. #19153747 | C22 | semidirect |
| 32. C4⋊#13089678 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153739 | C22 | semidirect |
| 37. C8×Dic181 | C22 | semidirect |
| 38. C4⋊Q8×C181 | C22 | semidirect |
| 40. #106×C181 | C22 | semidirect |
| 41. C4⋊C8×C181 | C22 | semidirect |
| 105. C4×D181 | SD16 | semidirect |
| 146. C181 | #3101 | semidirect |
| 152. #476 | D181 | semidirect |
| 164. C4⋊Q8 | C2×D181 | semidirect |
| 181. #106 | C2×D181 | semidirect |
| 183. C4⋊C8 | C2×D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041834 | 2 |
| C4×D4×D181 | 2 |
| #26041611 | 2 |
| #26041566 | 2 |
| #26041485 | 2 |
| #26041484 | 2 |
| #26041431 | 2 |
| #26041370 | 2 |
| #26041366 | 2 |
| #26041331 | 2 |
| #476×C181 | 2 |
| #3101 | 181 |