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. #26012115 | C2 | semidirect |
| 2. #26011875 | C2 | semidirect |
| 3. #26011853 | C2 | semidirect |
| 4. #26011738 | C2 | semidirect |
| 5. #26011733 | C2 | semidirect |
| 7. #26011590 | C2 | semidirect |
| 8. #26011585 | C2 | semidirect |
| 9. #26011573 | C2 | semidirect |
| 10. #26011445 | C2 | semidirect |
| 11. #500×C173 | C2 | semidirect |
| 117. C173 | #3175 | semidirect |
| 120. #500 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012115 | 2 |
| #26011875 | 2 |
| #26011853 | 2 |
| #26011738 | 2 |
| #26011733 | 2 |
| #26011728 | 2 |
| #26011590 | 2 |
| #26011585 | 2 |
| #26011573 | 2 |
| #26011445 | 2 |
| #500×C173 | 2 |
| #3175 | 173 |