Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 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. #26012104 | C2 | semidirect |
| 3. #26011864 | C2 | semidirect |
| 4. #26011861 | C2 | semidirect |
| 5. #26011857 | C2 | semidirect |
| 6. #26011738 | C2 | semidirect |
| 7. #26011721 | C2 | semidirect |
| 8. #26011590 | C2 | semidirect |
| 9. #26011578 | C2 | semidirect |
| 10. #26011445 | C2 | semidirect |
| 11. #499×C173 | C2 | semidirect |
| 108. C173 | #3174 | semidirect |
| 112. #499 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012104 | 2 |
| #26012097 | 2 |
| #26011864 | 2 |
| #26011861 | 2 |
| #26011857 | 2 |
| #26011738 | 2 |
| #26011721 | 2 |
| #26011590 | 2 |
| #26011578 | 2 |
| #26011445 | 2 |
| #499×C173 | 2 |
| #3174 | 173 |