Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19149704 | C2 | semidirect |
| 2. C2×#19149685 | C2 | semidirect |
| 3. #26012069 | C2 | semidirect |
| 4. #26012060 | C2 | semidirect |
| 5. #26011743 | C2 | semidirect |
| 6. #26011740 | C2 | semidirect |
| 7. #26011726 | C2 | semidirect |
| 8. #26011723 | C2 | semidirect |
| 9. #26011534 | C2 | semidirect |
| 10. C2×#19149601 | C2 | semidirect |
| 11. #416×C173 | C2 | semidirect |
| 19. C2×#14583809 | C22 | semidirect |
| 20. C2×C8×D173 | C22 | semidirect |
| 24. #19149655 | C22 | semidirect |
| 29. #19149650 | C22 | semidirect |
| 32. #19149612 | C22 | semidirect |
| 33. #19149610 | C22 | semidirect |
| 39. #103×C173 | C22 | semidirect |
| 40. #103×C173 | C22 | semidirect |
| 41. #102×C173 | C22 | semidirect |
| 42. #102×C173 | C22 | semidirect |
| 60. #14583810 | D4 | semidirect |
| 151. C173 | #3062 | semidirect |
| 162. #416 | D173 | semidirect |
| 189. #103 | C2×D173 | semidirect |
| 190. #103 | C2×D173 | semidirect |
| 193. #102 | C2×D173 | semidirect |
| 194. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149704 | 2 |
| C2×#19149685 | 2 |
| #26012069 | 2 |
| #26012060 | 2 |
| #26011743 | 2 |
| #26011740 | 2 |
| #26011726 | 2 |
| #26011723 | 2 |
| #26011534 | 2 |
| C2×#19149601 | 2 |
| #416×C173 | 2 |
| #3062 | 173 |