Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
548 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19149707 | C2 | semidirect |
| 2. C2×#19149704 | C2 | semidirect |
| 3. #26012037 | C2 | semidirect |
| 4. C2×#19149641 | C2 | semidirect |
| 5. #26011709 | C2 | semidirect |
| 6. #26011705 | C2 | semidirect |
| 7. #26011695 | C2 | semidirect |
| 8. #26011685 | C2 | semidirect |
| 9. #26011514 | C2 | semidirect |
| 10. #26011490 | C2 | semidirect |
| 11. #417×C173 | C2 | semidirect |
| 22. #19149677 | C22 | semidirect |
| 23. #19149675 | C22 | semidirect |
| 24. #19149668 | C22 | semidirect |
| 25. #19149666 | C22 | semidirect |
| 36. #19149608 | C22 | semidirect |
| 37. #19149608 | C22 | semidirect |
| 38. #19149602 | C22 | semidirect |
| 39. #19149599 | C22 | semidirect |
| 43. #103×C173 | C22 | semidirect |
| 44. #102×C173 | C22 | semidirect |
| 51. C2×D692 | D4 | semidirect |
| 158. Dic173 | AGL(1,ℤ/8) | semidirect |
| 166. C173 | #3036 | semidirect |
| 178. #417 | D173 | semidirect |
| 209. #103 | C2×D173 | semidirect |
| 211. #102 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149707 | 2 |
| C2×#19149704 | 2 |
| #26012037 | 2 |
| C2×#19149641 | 2 |
| #26011709 | 2 |
| #26011705 | 2 |
| #26011695 | 2 |
| #26011685 | 2 |
| #26011514 | 2 |
| #26011490 | 2 |
| #417×C173 | 2 |
| #3036 | 173 |