Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14583815 | C2 | semidirect |
| 2. C2×#19149685 | C2 | semidirect |
| 3. #26012067 | C2 | semidirect |
| 5. #26011738 | C2 | semidirect |
| 6. #26011721 | C2 | semidirect |
| 7. #26011499 | C2 | semidirect |
| 8. #26011495 | C2 | semidirect |
| 9. #427×C173 | C2 | semidirect |
| 18. C2×#14583809 | C22 | semidirect |
| 19. C2×C8×D173 | C22 | semidirect |
| 25. #19149659 | C22 | semidirect |
| 28. #19149602 | C22 | semidirect |
| 33. #107×C173 | C22 | semidirect |
| 34. #106×C173 | C22 | semidirect |
| 62. C2×C8×C173 | D4 | semidirect |
| 120. C173 | #3057 | semidirect |
| 128. #427 | D173 | semidirect |
| 152. #107 | C2×D173 | semidirect |
| 153. #106 | C2×D173 | semidirect |
| 180. C2×C8 | D692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583815 | 2 |
| C2×#19149685 | 2 |
| #26012067 | 2 |
| #26012060 | 2 |
| #26011738 | 2 |
| #26011721 | 2 |
| #26011499 | 2 |
| #26011495 | 2 |
| #427×C173 | 2 |
| #3057 | 173 |