Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 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. #26012305 | C2 | semidirect |
| 2. #26012302 | C2 | semidirect |
| 3. #26011874 | C2 | semidirect |
| 4. #26011766 | C2 | semidirect |
| 5. #26011758 | C2 | semidirect |
| 6. #26011752 | C2 | semidirect |
| 7. #26011669 | C2 | semidirect |
| 8. #26011662 | C2 | semidirect |
| 9. #26011608 | C2 | semidirect |
| 10. #26011606 | C2 | semidirect |
| 11. #576×C173 | C2 | semidirect |
| 12. #19149726 | C22 | semidirect |
| 15. #19149709 | C22 | semidirect |
| 18. #19149705 | C22 | semidirect |
| 22. C2×Dic692 | C22 | semidirect |
| 25. C2×#14583814 | C22 | semidirect |
| 26. #19149686 | C22 | semidirect |
| 27. #19149685 | C22 | semidirect |
| 28. #19149666 | C22 | semidirect |
| 29. #19149615 | C22 | semidirect |
| 30. #19149614 | C22 | semidirect |
| 32. #19149606 | C22 | semidirect |
| 33. #19149605 | C22 | semidirect |
| 34. #19149597 | C22 | semidirect |
| 35. #19149596 | C22 | semidirect |
| 36. C8×Dic173 | C22 | semidirect |
| 149. C173 | #3290 | semidirect |
| 153. #576 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012305 | 2 |
| #26012302 | 2 |
| #26011874 | 2 |
| #26011766 | 2 |
| #26011758 | 2 |
| #26011752 | 2 |
| #26011669 | 2 |
| #26011662 | 2 |
| #26011608 | 2 |
| #26011606 | 2 |
| #576×C173 | 2 |
| #3290 | 173 |