Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 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. #26012048 | C2 | semidirect |
| 3. #26011885 | C2 | semidirect |
| 4. #26011851 | C2 | semidirect |
| 5. #26011714 | C2 | semidirect |
| 6. #26011649 | C2 | semidirect |
| 8. #432×C173 | C2 | semidirect |
| 11. C2×Dic692 | C22 | semidirect |
| 13. #19149679 | C22 | semidirect |
| 14. #19149679 | C22 | semidirect |
| 23. C4×Dic346 | C22 | semidirect |
| 27. #19149604 | C22 | semidirect |
| 30. C4⋊C8×C173 | C22 | semidirect |
| 32. #97×C173 | C22 | semidirect |
| 112. C173 | #3215 | semidirect |
| 121. #432 | D173 | semidirect |
| 141. C4⋊C8 | C2×D173 | semidirect |
| 145. #97 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012048 | 2 |
| C2×#19149667 | 2 |
| #26011885 | 2 |
| #26011851 | 2 |
| #26011714 | 2 |
| #26011649 | 2 |
| #26011644 | 2 |
| #432×C173 | 2 |
| #3215 | 173 |