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. #26012039 | C2 | semidirect |
| 2. #26012020 | C2 | semidirect |
| 3. #26011886 | C2 | semidirect |
| 4. #26011860 | C2 | semidirect |
| 5. #26011855 | C2 | semidirect |
| 6. #26011711 | C2 | semidirect |
| 7. #26011704 | C2 | semidirect |
| 8. #26011650 | C2 | semidirect |
| 9. #26011633 | C2 | semidirect |
| 10. #26011546 | C2 | semidirect |
| 11. #496×C173 | C2 | semidirect |
| 140. C173 | #3219 | semidirect |
| 145. #496 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012039 | 2 |
| #26012020 | 2 |
| #26011886 | 2 |
| #26011860 | 2 |
| #26011855 | 2 |
| #26011711 | 2 |
| #26011704 | 2 |
| #26011650 | 2 |
| #26011633 | 2 |
| #26011546 | 2 |
| #496×C173 | 2 |
| #3219 | 173 |