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×#19149704 | C2 | semidirect |
| 2. C2×M16×D173 | C2 | semidirect |
| 3. #26011998 | C2 | semidirect |
| 4. C2×#19149654 | C2 | semidirect |
| 5. #26011743 | C2 | semidirect |
| 6. #26011740 | C2 | semidirect |
| 7. #26011726 | C2 | semidirect |
| 8. #26011723 | C2 | semidirect |
| 9. #26011531 | C2 | semidirect |
| 10. #26011497 | C2 | semidirect |
| 11. #417×C173 | C2 | semidirect |
| 16. C2×#14583813 | C22 | semidirect |
| 17. C2×#14583811 | C22 | semidirect |
| 19. C2×#14583809 | C22 | semidirect |
| 21. C2×C8×D173 | C22 | semidirect |
| 23. #19149655 | C22 | semidirect |
| 24. #19149655 | C22 | semidirect |
| 29. #19149650 | C22 | semidirect |
| 30. #19149650 | C22 | semidirect |
| 36. #19149612 | C22 | semidirect |
| 37. #19149610 | C22 | semidirect |
| 38. #19149601 | C22 | semidirect |
| 39. #19149601 | C22 | semidirect |
| 43. #103×C173 | C22 | semidirect |
| 44. #102×C173 | C22 | semidirect |
| 65. #14583810 | D4 | semidirect |
| 120. #13063436 | C2×D4 | semidirect |
| 154. C2×D173 | AGL(1,ℤ/8) | semidirect |
| 172. C173 | #3055 | semidirect |
| 184. #417 | D173 | semidirect |
| 214. #103 | C2×D173 | semidirect |
| 217. #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×M16×D173 | 2 |
| #26011998 | 2 |
| C2×#19149654 | 2 |
| #26011743 | 2 |
| #26011740 | 2 |
| #26011726 | 2 |
| #26011723 | 2 |
| #26011531 | 2 |
| #26011497 | 2 |
| #417×C173 | 2 |
| #3055 | 173 |