Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#19149704 | C2 | semidirect |
| 2. C2×#19149686 | C2 | semidirect |
| 3. #26012055 | C2 | semidirect |
| 4. #26011742 | C2 | semidirect |
| 5. #26011739 | C2 | semidirect |
| 6. #26011725 | C2 | semidirect |
| 7. #26011722 | C2 | semidirect |
| 8. #26011531 | C2 | semidirect |
| 9. #26011487 | C2 | semidirect |
| 10. C2×#19149599 | C2 | semidirect |
| 11. #537×C173 | C2 | semidirect |
| 18. C2×#14583810 | C22 | semidirect |
| 20. C22×#13063436 | C22 | semidirect |
| 27. #19149612 | C22 | semidirect |
| 28. #19149610 | C22 | semidirect |
| 29. #19149603 | C22 | semidirect |
| 30. #19149603 | C22 | semidirect |
| 31. #19149600 | C22 | semidirect |
| 32. #19149600 | C22 | semidirect |
| 38. C22⋊Q8×C173 | C22 | semidirect |
| 41. #121×C173 | C22 | semidirect |
| 53. #14583810 | D4 | semidirect |
| 151. C173 | #3062 | semidirect |
| 155. #537 | D173 | semidirect |
| 178. C22⋊Q8 | C2×D173 | semidirect |
| 183. #121 | 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×#19149686 | 2 |
| #26012055 | 2 |
| #26011742 | 2 |
| #26011739 | 2 |
| #26011725 | 2 |
| #26011722 | 2 |
| #26011531 | 2 |
| #26011487 | 2 |
| C2×#19149599 | 2 |
| #537×C173 | 2 |
| #3062 | 173 |