Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #26011773 | C2 | semidirect |
| 5. #26011702 | C2 | semidirect |
| 6. #26011701 | C2 | semidirect |
| 8. #26011597 | C2 | semidirect |
| 9. #26011595 | C2 | semidirect |
| 11. #475×C173 | C2 | semidirect |
| 132. C173 | #3113 | semidirect |
| 138. #475 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| C4×Q8×D173 | 2 |
| #26011823 | 2 |
| #26011773 | 2 |
| #26011702 | 2 |
| #26011701 | 2 |
| #26011648 | 2 |
| #26011597 | 2 |
| #26011595 | 2 |
| #26011547 | 2 |
| #475×C173 | 2 |
| #3113 | 173 |