Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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. #26012122 | C2 | semidirect |
| 3. #26011794 | C2 | semidirect |
| 4. #26011790 | C2 | semidirect |
| 5. #26011780 | C2 | semidirect |
| 6. #26011770 | C2 | semidirect |
| 7. #26011527 | C2 | semidirect |
| 8. #26011519 | C2 | semidirect |
| 11. #428×C173 | C2 | semidirect |
| 15. #19149678 | C22 | semidirect |
| 17. #19149670 | C22 | semidirect |
| 26. #19149612 | C22 | semidirect |
| 27. #19149612 | C22 | semidirect |
| 28. #19149610 | C22 | semidirect |
| 29. #19149610 | C22 | semidirect |
| 30. #19149608 | C22 | semidirect |
| 31. #19149608 | C22 | semidirect |
| 39. #107×C173 | C22 | semidirect |
| 40. #106×C173 | C22 | semidirect |
| 45. C2×D692 | Q8 | semidirect |
| 124. C173 | #3081 | semidirect |
| 132. #428 | D173 | semidirect |
| 156. #107 | C2×D173 | semidirect |
| 159. #106 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012122 | 2 |
| #26011965 | 2 |
| #26011794 | 2 |
| #26011790 | 2 |
| #26011780 | 2 |
| #26011770 | 2 |
| #26011527 | 2 |
| #26011519 | 2 |
| #26011497 | 2 |
| C2×#19149599 | 2 |
| #428×C173 | 2 |
| #3081 | 173 |