Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
404 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 2. C4⋊Q8×D173 | C2 | semidirect |
| 3. #26011895 | C2 | semidirect |
| 4. #26011836 | C2 | semidirect |
| 5. #26011806 | C2 | semidirect |
| 6. #26011803 | C2 | semidirect |
| 7. #26011772 | C2 | semidirect |
| 8. #26011771 | C2 | semidirect |
| 9. #26011768 | C2 | semidirect |
| 10. #26011543 | C2 | semidirect |
| 11. #474×C173 | C2 | semidirect |
| 141. C173 | #3226 | semidirect |
| 152. #474 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012038 | 2 |
| C4⋊Q8×D173 | 2 |
| #26011895 | 2 |
| #26011836 | 2 |
| #26011806 | 2 |
| #26011803 | 2 |
| #26011772 | 2 |
| #26011771 | 2 |
| #26011768 | 2 |
| #26011543 | 2 |
| #474×C173 | 2 |
| #3226 | 173 |