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×#13133206 | C2 | semidirect |
| 3. #16811009 | C2 | semidirect |
| 4. #16810984 | C2 | semidirect |
| 5. #16810841 | C2 | semidirect |
| 6. #16810840 | C2 | semidirect |
| 7. #16810762 | C2 | semidirect |
| 8. #16810759 | C2 | semidirect |
| 9. #16810756 | C2 | semidirect |
| 10. #16810677 | C2 | semidirect |
| 11. C53×#448 | C2 | semidirect |
| 14. C2×#11719924 | C22 | semidirect |
| 17. #13133216 | C22 | semidirect |
| 18. #13133213 | C22 | semidirect |
| 26. D4×Dic53 | C22 | semidirect |
| 27. #13133179 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133141 | C22 | semidirect |
| 37. #13133127 | C22 | semidirect |
| 39. C2×SD16×C53 | C22 | semidirect |
| 41. #103×C53 | C22 | semidirect |
| 160. #448 | D53 | semidirect |
| 164. C53 | #3213 | semidirect |
| 169. C2×SD16 | C2×D53 | semidirect |
| 190. #103 | C2×D53 | semidirect |