Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26012102 | C2 | semidirect |
| 3. #26011890 | C2 | semidirect |
| 4. #26011865 | C2 | semidirect |
| 5. #26011856 | C2 | semidirect |
| 6. #26011740 | C2 | semidirect |
| 7. #26011723 | C2 | semidirect |
| 8. #26011594 | C2 | semidirect |
| 9. #26011576 | C2 | semidirect |
| 10. #26011448 | C2 | semidirect |
| 11. #491×C173 | C2 | semidirect |
| 108. C173 | #3174 | semidirect |
| 114. #491 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012102 | 2 |
| #26012097 | 2 |
| #26011890 | 2 |
| #26011865 | 2 |
| #26011856 | 2 |
| #26011740 | 2 |
| #26011723 | 2 |
| #26011594 | 2 |
| #26011576 | 2 |
| #26011448 | 2 |
| #491×C173 | 2 |
| #3174 | 173 |