Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 1. Q8×Dic346 | C2 | semidirect |
| 4. #26011842 | C2 | semidirect |
| 6. #26011777 | C2 | semidirect |
| 8. #26011702 | C2 | semidirect |
| 9. #26011599 | C2 | semidirect |
| 11. #446×C173 | C2 | semidirect |
| 116. C173 | #3369 | semidirect |
| 126. #446 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic346 | 2 |
| #26012214 | 2 |
| #26011851 | 2 |
| #26011842 | 2 |
| #26011782 | 2 |
| #26011777 | 2 |
| #26011714 | 2 |
| #26011702 | 2 |
| #26011599 | 2 |
| C4×#14583815 | 2 |
| #446×C173 | 2 |
| #3369 | 173 |