Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 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. #26012036 | C2 | semidirect |
| 2. C2×#19149675 | C2 | semidirect |
| 3. #26011866 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011685 | C2 | semidirect |
| 6. #26011684 | C2 | semidirect |
| 7. #26011627 | C2 | semidirect |
| 8. #26011625 | C2 | semidirect |
| 9. #26011624 | C2 | semidirect |
| 10. #26011541 | C2 | semidirect |
| 11. #447×C173 | C2 | semidirect |
| 16. C2×D1384 | C22 | semidirect |
| 17. C2×#14583811 | C22 | semidirect |
| 18. C2×#14583811 | C22 | semidirect |
| 19. #19149678 | C22 | semidirect |
| 24. #19149675 | C22 | semidirect |
| 28. D4×Dic173 | C22 | semidirect |
| 29. #19149641 | 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×D8×C173 | C22 | semidirect |
| 41. #102×C173 | C22 | semidirect |
| 107. C2×Dic173 | D8 | semidirect |
| 164. C173 | #3205 | semidirect |
| 175. #447 | D173 | semidirect |
| 185. C2×D8 | C2×D173 | semidirect |
| 204. #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×#19149675 | 2 |
| #26011866 | 2 |
| #26011836 | 2 |
| #26011685 | 2 |
| #26011684 | 2 |
| #26011627 | 2 |
| #26011625 | 2 |
| #26011624 | 2 |
| #26011541 | 2 |
| #447×C173 | 2 |
| #3205 | 173 |