Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26012041 | C2 | semidirect |
| 2. #26012025 | C2 | semidirect |
| 3. #26011885 | C2 | semidirect |
| 4. #26011880 | C2 | semidirect |
| 5. #26011860 | C2 | semidirect |
| 6. #26011856 | C2 | semidirect |
| 7. #26011714 | C2 | semidirect |
| 8. #26011707 | C2 | semidirect |
| 9. #26011655 | C2 | semidirect |
| 10. #26011638 | C2 | semidirect |
| 11. #432×C173 | C2 | semidirect |
| 140. C173 | #3219 | semidirect |
| 152. #432 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012041 | 2 |
| #26012025 | 2 |
| #26011885 | 2 |
| #26011880 | 2 |
| #26011860 | 2 |
| #26011856 | 2 |
| #26011714 | 2 |
| #26011707 | 2 |
| #26011655 | 2 |
| #26011638 | 2 |
| #432×C173 | 2 |
| #3219 | 173 |