Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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. #16811154 | C2 | semidirect |
| 2. C2×#13133179 | C2 | semidirect |
| 3. #16810953 | C2 | semidirect |
| 4. #16810926 | C2 | semidirect |
| 5. #16810837 | C2 | semidirect |
| 6. #16810776 | C2 | semidirect |
| 8. #16810732 | C2 | semidirect |
| 9. #16810722 | C2 | semidirect |
| 10. #16810677 | C2 | semidirect |
| 11. C53×#480 | C2 | semidirect |
| 17. #13133208 | C22 | semidirect |
| 18. #13133204 | C22 | semidirect |
| 21. #13133182 | C22 | semidirect |
| 23. D4×Dic53 | C22 | semidirect |
| 31. #13133148 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133140 | C22 | semidirect |
| 37. #13133127 | C22 | semidirect |
| 40. #107×C53 | C22 | semidirect |
| 41. #102×C53 | C22 | semidirect |
| 144. #480 | D53 | semidirect |
| 152. C53 | #3114 | semidirect |
| 174. #107 | C2×D53 | semidirect |
| 180. #102 | C2×D53 | semidirect |