Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26012036 | C2 | semidirect |
| 2. C2×#19149641 | C2 | semidirect |
| 3. #26011804 | C2 | semidirect |
| 4. #26011770 | C2 | semidirect |
| 5. #26011685 | C2 | semidirect |
| 6. #26011627 | C2 | semidirect |
| 7. #26011624 | C2 | semidirect |
| 8. #26011573 | C2 | semidirect |
| 9. #26011571 | C2 | semidirect |
| 10. #26011541 | C2 | semidirect |
| 11. #480×C173 | C2 | semidirect |
| 17. #19149678 | C22 | semidirect |
| 18. #19149675 | C22 | semidirect |
| 22. D4×Dic173 | C22 | semidirect |
| 27. #19149641 | C22 | semidirect |
| 31. #19149612 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 37. C8×Dic173 | C22 | semidirect |
| 40. #107×C173 | C22 | semidirect |
| 41. #102×C173 | C22 | semidirect |
| 92. D692 | #41 | semidirect |
| 99. C2×Dic173 | D8 | semidirect |
| 149. C173 | #3100 | semidirect |
| 154. #480 | D173 | semidirect |
| 184. #107 | C2×D173 | semidirect |
| 189. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012036 | 2 |
| C2×#19149641 | 2 |
| #26011804 | 2 |
| #26011770 | 2 |
| #26011685 | 2 |
| #26011627 | 2 |
| #26011624 | 2 |
| #26011573 | 2 |
| #26011571 | 2 |
| #26011541 | 2 |
| #480×C173 | 2 |
| #3100 | 173 |