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. #26012038 | C2 | semidirect |
| 2. #127×D173 | C2 | semidirect |
| 3. #26011866 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011687 | C2 | semidirect |
| 6. #26011686 | C2 | semidirect |
| 7. #26011683 | C2 | semidirect |
| 8. #26011626 | C2 | semidirect |
| 9. #26011623 | C2 | semidirect |
| 10. #26011543 | C2 | semidirect |
| 11. #459×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 |
| 29. C4×D692 | C22 | semidirect |
| 32. C4⋊#13063436 | C22 | semidirect |
| 33. #19149601 | C22 | semidirect |
| 34. #19149600 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 37. C8×Dic173 | C22 | semidirect |
| 38. C2×D8×C173 | C22 | semidirect |
| 40. C4×D4×C173 | C22 | semidirect |
| 41. C4⋊C8×C173 | C22 | semidirect |
| 42. #102×C173 | C22 | semidirect |
| 115. C4×D173 | D8 | semidirect |
| 165. C173 | #3205 | semidirect |
| 174. #459 | D173 | semidirect |
| 185. C2×D8 | C2×D173 | semidirect |
| 199. C4×D4 | C2×D173 | semidirect |
| 202. C4⋊C8 | C2×D173 | semidirect |
| 206. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012038 | 2 |
| #127×D173 | 2 |
| #26011866 | 2 |
| #26011836 | 2 |
| #26011687 | 2 |
| #26011686 | 2 |
| #26011683 | 2 |
| #26011626 | 2 |
| #26011623 | 2 |
| #26011543 | 2 |
| #459×C173 | 2 |
| #3205 | 173 |