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 |
|---|---|---|
| 1. #26012020 | C2 | semidirect |
| 2. #26011893 | C2 | semidirect |
| 3. #26011845 | C2 | semidirect |
| 4. #26011729 | C2 | semidirect |
| 6. #26011717 | C2 | semidirect |
| 7. Q16×Dic173 | C2 | semidirect |
| 8. SD16×Dic173 | C2 | semidirect |
| 9. D8×Dic173 | C2 | semidirect |
| 10. C4×C8×D173 | C2 | semidirect |
| 11. #495×C173 | C2 | semidirect |
| 118. C173 | #3168 | semidirect |
| 122. #495 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012020 | 2 |
| #26011893 | 2 |
| #26011845 | 2 |
| #26011729 | 2 |
| #26011724 | 2 |
| #26011717 | 2 |
| Q16×Dic173 | 2 |
| SD16×Dic173 | 2 |
| D8×Dic173 | 2 |
| C4×C8×D173 | 2 |
| #495×C173 | 2 |
| #3168 | 173 |