Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26012042 | C2 | semidirect |
| 2. #26012020 | C2 | semidirect |
| 3. #26011881 | C2 | semidirect |
| 4. #26011859 | C2 | semidirect |
| 5. #26011856 | C2 | semidirect |
| 6. #26011715 | C2 | semidirect |
| 7. #26011708 | C2 | semidirect |
| 8. #26011652 | C2 | semidirect |
| 9. #26011635 | C2 | semidirect |
| 10. #26011546 | C2 | semidirect |
| 11. #497×C173 | C2 | semidirect |
| 140. C173 | #3219 | semidirect |
| 144. #497 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012042 | 2 |
| #26012020 | 2 |
| #26011881 | 2 |
| #26011859 | 2 |
| #26011856 | 2 |
| #26011715 | 2 |
| #26011708 | 2 |
| #26011652 | 2 |
| #26011635 | 2 |
| #26011546 | 2 |
| #497×C173 | 2 |
| #3219 | 173 |