Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 121 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. #26041810 | C2 | semidirect |
| 2. C2×D4×Dic181 | C2 | semidirect |
| 3. #26041610 | C2 | semidirect |
| 4. #26041590 | C2 | semidirect |
| 5. #26041581 | C2 | semidirect |
| 6. #26041492 | C2 | semidirect |
| 7. #26041430 | C2 | semidirect |
| 8. #26041391 | C2 | semidirect |
| 9. #26041376 | C2 | semidirect |
| 10. #26041333 | C2 | semidirect |
| 15. #19153807 | C22 | semidirect |
| 16. #19153803 | C22 | semidirect |
| 19. #19153781 | C22 | semidirect |
| 25. D4×Dic181 | C22 | semidirect |
| 30. #19153749 | C22 | semidirect |
| 31. #19153748 | C22 | semidirect |
| 32. #19153745 | C22 | semidirect |
| 33. #19153741 | C22 | semidirect |
| 35. #19153737 | C22 | semidirect |
| 37. #19153726 | C22 | semidirect |
| 140. C181 | #3114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041810 | 2 |
| C2×D4×Dic181 | 2 |
| #26041610 | 2 |
| #26041590 | 2 |
| #26041581 | 2 |
| #26041492 | 2 |
| #26041430 | 2 |
| #26041391 | 2 |
| #26041376 | 2 |
| #26041333 | 2 |
| #447×C181 | 2 |
| #3114 | 181 |