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×#19149705 | C2 | semidirect |
| 2. C2×#19149685 | C2 | semidirect |
| 3. #26012072 | C2 | semidirect |
| 4. #26012058 | C2 | semidirect |
| 5. #26011743 | C2 | semidirect |
| 6. #26011736 | C2 | semidirect |
| 7. #26011726 | C2 | semidirect |
| 8. #26011719 | C2 | semidirect |
| 9. #26011531 | C2 | semidirect |
| 10. #26011488 | C2 | semidirect |
| 11. C2×#102×C173 | C2 | semidirect |
| 19. C2×#14583809 | C22 | semidirect |
| 20. C2×C8×D173 | C22 | semidirect |
| 24. #19149659 | C22 | semidirect |
| 26. #19149654 | C22 | semidirect |
| 32. #19149612 | C22 | semidirect |
| 33. #19149610 | C22 | semidirect |
| 34. #19149604 | C22 | semidirect |
| 35. #19149604 | C22 | semidirect |
| 36. #19149601 | C22 | semidirect |
| 37. #19149601 | C22 | semidirect |
| 60. #14583810 | D4 | semidirect |
| 151. C173 | #3062 | semidirect |
| 163. C2×#102 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149705 | 2 |
| C2×#19149685 | 2 |
| #26012072 | 2 |
| #26012058 | 2 |
| #26011743 | 2 |
| #26011736 | 2 |
| #26011726 | 2 |
| #26011719 | 2 |
| #26011531 | 2 |
| #26011488 | 2 |
| C2×#102×C173 | 2 |
| #3062 | 173 |