Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #26011507 | C2 | semidirect |
| 3. #26011487 | C2 | semidirect |
| 4. #26011459 | C2 | semidirect |
| 5. #26011262 | C2 | semidirect |
| 6. #26011255 | C2 | semidirect |
| 7. #568×C173 | C2 | semidirect |
| 10. #19149709 | C4 | semidirect |
| 12. #19149704 | C4 | semidirect |
| 118. C173 | #1881 | semidirect |
| 121. #568 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012289 | 2 |
| #26011507 | 2 |
| #26011487 | 2 |
| #26011459 | 2 |
| #26011262 | 2 |
| #26011255 | 2 |
| #568×C173 | 2 |
| #1881 | 173 |