Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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. C4⋊Q8×D173 | C2 | semidirect |
| 3. #26011886 | C2 | semidirect |
| 4. #26011860 | C2 | semidirect |
| 5. #26011859 | C2 | semidirect |
| 6. #26011699 | C2 | semidirect |
| 7. #26011694 | C2 | semidirect |
| 8. #26011645 | C2 | semidirect |
| 10. #26011546 | C2 | semidirect |
| 11. #497×C173 | C2 | semidirect |
| 135. C173 | #3218 | semidirect |
| 140. #497 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D173 | 2 |
| #26012020 | 2 |
| #26011886 | 2 |
| #26011860 | 2 |
| #26011859 | 2 |
| #26011699 | 2 |
| #26011694 | 2 |
| #26011645 | 2 |
| #26011628 | 2 |
| #26011546 | 2 |
| #497×C173 | 2 |
| #3218 | 173 |