Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
444 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 444 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. #16811168 | C2 | semidirect |
| 2. C2×#13133204 | C2 | semidirect |
| 3. #16811011 | C2 | semidirect |
| 4. #16810981 | C2 | semidirect |
| 5. #16810837 | C2 | semidirect |
| 6. #16810836 | C2 | semidirect |
| 7. #16810764 | C2 | semidirect |
| 8. #16810761 | C2 | semidirect |
| 9. #16810757 | C2 | semidirect |
| 10. #16810677 | C2 | semidirect |
| 11. C53×#447 | C2 | semidirect |
| 14. C2×#11719913 | C22 | semidirect |
| 15. C2×#11719923 | C22 | semidirect |
| 17. #13133216 | C22 | semidirect |
| 18. #13133213 | C22 | semidirect |
| 26. D4×Dic53 | C22 | semidirect |
| 27. #13133179 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133142 | C22 | semidirect |
| 34. #13133140 | C22 | semidirect |
| 37. #13133127 | C22 | semidirect |
| 162. #447 | D53 | semidirect |
| 164. C53 | #3213 | semidirect |