Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26012043 | C2 | semidirect |
| 3. #26011862 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011690 | C2 | semidirect |
| 6. #26011689 | C2 | semidirect |
| 7. #26011644 | C2 | semidirect |
| 8. #26011642 | C2 | semidirect |
| 9. #26011641 | C2 | semidirect |
| 10. #26011541 | C2 | semidirect |
| 11. #450×C173 | C2 | semidirect |
| 15. C2×#14583815 | C22 | semidirect |
| 16. C2×#14583814 | C22 | semidirect |
| 17. C2×#14583813 | C22 | semidirect |
| 18. #19149678 | C22 | semidirect |
| 19. #19149677 | C22 | semidirect |
| 27. Q8×Dic173 | C22 | semidirect |
| 29. #19149644 | C22 | semidirect |
| 32. #19149608 | C22 | semidirect |
| 33. #19149601 | C22 | semidirect |
| 34. #19149600 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 37. C8×Dic173 | C22 | semidirect |
| 39. C2×SD16×C173 | C22 | semidirect |
| 41. #102×C173 | C22 | semidirect |
| 102. C2×Dic173 | SD16 | semidirect |
| 151. C173 | #3208 | semidirect |
| 162. #450 | D173 | semidirect |
| 171. C2×SD16 | C2×D173 | semidirect |
| 191. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012043 | 2 |
| C2×#19149675 | 2 |
| #26011862 | 2 |
| #26011836 | 2 |
| #26011690 | 2 |
| #26011689 | 2 |
| #26011644 | 2 |
| #26011642 | 2 |
| #26011641 | 2 |
| #26011541 | 2 |
| #450×C173 | 2 |
| #3208 | 173 |