Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #26012291 | C2 | semidirect |
| 2. C2×#19149707 | C2 | semidirect |
| 3. C2×#19149707 | C2 | semidirect |
| 4. #26012257 | C2 | semidirect |
| 5. #26011762 | C2 | semidirect |
| 6. #26011755 | C2 | semidirect |
| 7. #26011473 | C2 | semidirect |
| 8. C2×#19149595 | C2 | semidirect |
| 9. #430×C173 | C2 | semidirect |
| 14. #19149712 | C22 | semidirect |
| 20. #19149707 | C22 | semidirect |
| 23. C2×#14583815 | C22 | semidirect |
| 25. C2×D1384 | C22 | semidirect |
| 27. #19149685 | C22 | semidirect |
| 30. #19149597 | C22 | semidirect |
| 31. #19149595 | C22 | semidirect |
| 32. #19149595 | C22 | semidirect |
| 36. #108×C173 | C22 | semidirect |
| 147. C173 | #3068 | semidirect |
| 155. #430 | D173 | semidirect |
| 181. #108 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012291 | 2 |
| C2×#19149707 | 2 |
| #26012257 | 2 |
| #26011762 | 2 |
| #26011755 | 2 |
| #26011473 | 2 |
| C2×#19149595 | 2 |
| #430×C173 | 2 |
| #3068 | 173 |