Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
444 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 444 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. #26012308 | C2 | semidirect |
| 2. #26012307 | C2 | semidirect |
| 3. #26012304 | C2 | semidirect |
| 4. #26011869 | C2 | semidirect |
| 5. #26011767 | C2 | semidirect |
| 6. #26011765 | C2 | semidirect |
| 7. #26011676 | C2 | semidirect |
| 8. #26011672 | C2 | semidirect |
| 9. #26011607 | C2 | semidirect |
| 10. #26011606 | C2 | semidirect |
| 11. #473×C173 | C2 | semidirect |
| 146. C173 | #3293 | semidirect |
| 154. #473 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012308 | 2 |
| #26012307 | 2 |
| #26012304 | 2 |
| #26011869 | 2 |
| #26011767 | 2 |
| #26011765 | 2 |
| #26011676 | 2 |
| #26011672 | 2 |
| #26011607 | 2 |
| #26011606 | 2 |
| #473×C173 | 2 |
| #3293 | 173 |