Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
388 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 388 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. #26012095 | C2 | semidirect |
| 2. #26012061 | C2 | semidirect |
| 3. #26011863 | C2 | semidirect |
| 4. #26011860 | C2 | semidirect |
| 5. #26011845 | C2 | semidirect |
| 6. #26011704 | C2 | semidirect |
| 7. #26011694 | C2 | semidirect |
| 8. #26011633 | C2 | semidirect |
| 9. #26011628 | C2 | semidirect |
| 10. #26011553 | C2 | semidirect |
| 11. #496×C173 | C2 | semidirect |
| 120. C173 | #3221 | semidirect |
| 124. #496 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012095 | 2 |
| #26012061 | 2 |
| #26011863 | 2 |
| #26011860 | 2 |
| #26011845 | 2 |
| #26011704 | 2 |
| #26011694 | 2 |
| #26011633 | 2 |
| #26011628 | 2 |
| #26011553 | 2 |
| #496×C173 | 2 |
| #3221 | 173 |