Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 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. #16811154 | C2 | semidirect |
| 2. C2×#13133206 | C2 | semidirect |
| 3. #16811004 | C2 | semidirect |
| 4. #16810979 | C2 | semidirect |
| 5. #16810848 | C2 | semidirect |
| 6. #16810840 | C2 | semidirect |
| 7. #16810779 | C2 | semidirect |
| 8. #16810776 | C2 | semidirect |
| 10. #16810673 | C2 | semidirect |
| 11. C53×#448 | C2 | semidirect |
| 13. C2×#11719925 | C22 | semidirect |
| 17. #13133208 | C22 | semidirect |
| 22. #13133204 | C22 | semidirect |
| 25. #13133182 | C22 | semidirect |
| 27. D4×Dic53 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133141 | C22 | semidirect |
| 37. C8×Dic53 | C22 | semidirect |
| 39. C2×SD16×C53 | C22 | semidirect |
| 41. #103×C53 | C22 | semidirect |
| 152. #448 | D53 | semidirect |
| 155. C53 | #3211 | semidirect |
| 160. C2×SD16 | C2×D53 | semidirect |
| 181. #103 | C2×D53 | semidirect |