Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26041670 | C2 | semidirect |
| 4. #26041637 | C2 | semidirect |
| 5. #26041500 | C2 | semidirect |
| 6. #26041499 | C2 | semidirect |
| 7. #26041437 | C2 | semidirect |
| 8. #26041434 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 13. C2×Dic724 | C22 | semidirect |
| 14. C2×#15668439 | C22 | semidirect |
| 16. #19153815 | C22 | semidirect |
| 17. #19153814 | C22 | semidirect |
| 25. Q8×Dic181 | C22 | semidirect |
| 27. #19153781 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 34. #19153739 | C22 | semidirect |
| 37. #19153726 | C22 | semidirect |
| 139. C181 | #3215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041831 | 2 |
| C2×#19153803 | 2 |
| #26041670 | 2 |
| #26041637 | 2 |
| #26041500 | 2 |
| #26041499 | 2 |
| #26041437 | 2 |
| #26041434 | 2 |
| #26041430 | 2 |
| #26041333 | 2 |
| #450×C181 | 2 |
| #3215 | 181 |