Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
490 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 113 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. #127×D173 | C2 | semidirect |
| 2. #26012026 | C2 | semidirect |
| 3. #26011880 | C2 | semidirect |
| 4. #26011878 | C2 | semidirect |
| 5. #26011857 | C2 | semidirect |
| 6. #26011690 | C2 | semidirect |
| 7. #26011685 | C2 | semidirect |
| 8. #26011643 | C2 | semidirect |
| 9. #26011626 | C2 | semidirect |
| 10. #26011546 | C2 | semidirect |
| 11. #490×C173 | C2 | semidirect |
| 15. C2×#14583815 | C22 | semidirect |
| 16. C2×#14583814 | C22 | semidirect |
| 17. C2×D1384 | C22 | semidirect |
| 18. C2×#14583811 | C22 | semidirect |
| 24. #19149667 | C22 | semidirect |
| 28. #19149644 | C22 | semidirect |
| 30. #19149641 | C22 | semidirect |
| 33. #19149608 | C22 | semidirect |
| 34. #19149599 | C22 | semidirect |
| 35. #19149599 | C22 | semidirect |
| 37. #19149590 | C22 | semidirect |
| 39. #125×C173 | C22 | semidirect |
| 40. #102×C173 | C22 | semidirect |
| 41. #102×C173 | C22 | semidirect |
| 42. #97×C173 | C22 | semidirect |
| 152. C173 | #3217 | semidirect |
| 159. #490 | D173 | semidirect |
| 178. #125 | C2×D173 | semidirect |
| 191. #102 | C2×D173 | semidirect |
| 192. #102 | C2×D173 | semidirect |
| 195. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×D173 | 2 |
| #26012026 | 2 |
| #26011880 | 2 |
| #26011878 | 2 |
| #26011857 | 2 |
| #26011690 | 2 |
| #26011685 | 2 |
| #26011643 | 2 |
| #26011626 | 2 |
| #26011546 | 2 |
| #490×C173 | 2 |
| #3217 | 173 |