Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #16810961 | C2 | semidirect |
| 3. #16810953 | C2 | semidirect |
| 4. #16810936 | C2 | semidirect |
| 5. #16810862 | C2 | semidirect |
| 6. #16810854 | C2 | semidirect |
| 7. #16810783 | C2 | semidirect |
| 8. #16810779 | C2 | semidirect |
| 9. #16810762 | C2 | semidirect |
| 10. C2×C22⋊#88322 | C2 | semidirect |
| 11. C2×C22⋊Q8×C53 | C2 | semidirect |
| 13. C2×#11719925 | C22 | semidirect |
| 14. C2×#11719924 | C22 | semidirect |
| 25. #13133150 | C22 | semidirect |
| 26. #13133148 | C22 | semidirect |
| 27. #13133141 | C22 | semidirect |
| 28. #13133141 | C22 | semidirect |
| 29. #13133140 | C22 | semidirect |
| 30. #13133137 | C22 | semidirect |
| 151. C2×C22⋊Q8 | D53 | semidirect |
| 161. C53 | #3190 | semidirect |