Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 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. #26012002 | C2 | semidirect |
| 2. C2×#19149653 | C2 | semidirect |
| 3. #26011827 | C2 | semidirect |
| 4. #26011816 | C2 | semidirect |
| 5. #26011810 | C2 | semidirect |
| 6. #26011727 | C2 | semidirect |
| 7. #26011720 | C2 | semidirect |
| 8. #26011644 | C2 | semidirect |
| 9. #26011638 | C2 | semidirect |
| 10. #26011627 | C2 | semidirect |
| 11. C2×C22⋊C8×C173 | C2 | semidirect |
| 12. C2×#14583826 | C22 | semidirect |
| 15. C2×#14583815 | C22 | semidirect |
| 16. C2×D1384 | C22 | semidirect |
| 19. #19149658 | C22 | semidirect |
| 25. #19149653 | C22 | semidirect |
| 29. #19149638 | C22 | semidirect |
| 32. #19149613 | C22 | semidirect |
| 33. #19149611 | C22 | semidirect |
| 34. #19149604 | C22 | semidirect |
| 35. #19149601 | C22 | semidirect |
| 36. #19149601 | C22 | semidirect |
| 37. #19149601 | C22 | semidirect |
| 39. C22×C8×C173 | C22 | semidirect |
| 42. C22⋊C8×C173 | C22 | semidirect |
| 158. C173 | #3188 | semidirect |
| 170. C2×C22⋊C8 | D173 | semidirect |
| 177. C22×C8 | C2×D173 | semidirect |
| 201. C22⋊C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012002 | 2 |
| C2×#19149653 | 2 |
| #26011827 | 2 |
| #26011816 | 2 |
| #26011810 | 2 |
| #26011727 | 2 |
| #26011720 | 2 |
| #26011644 | 2 |
| #26011638 | 2 |
| #26011627 | 2 |
| C2×C22⋊C8×C173 | 2 |
| #3188 | 173 |