Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26012046 | C2 | semidirect |
| 3. #26011900 | C2 | semidirect |
| 4. #26011859 | C2 | semidirect |
| 5. #26011850 | C2 | semidirect |
| 6. #26011746 | C2 | semidirect |
| 8. Q16×Dic173 | C2 | semidirect |
| 9. SD16×Dic173 | C2 | semidirect |
| 10. #26011443 | C2 | semidirect |
| 11. #497×C173 | C2 | semidirect |
| 129. C173 | #3172 | semidirect |
| 134. #497 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| #26012020 | 2 |
| #26011900 | 2 |
| #26011859 | 2 |
| #26011850 | 2 |
| #26011746 | 2 |
| #26011734 | 2 |
| Q16×Dic173 | 2 |
| SD16×Dic173 | 2 |
| #26011443 | 2 |
| #497×C173 | 2 |
| #3172 | 173 |