Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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 |
|---|---|---|
| 1. #16811254 | C2 | semidirect |
| 3. #16810986 | C2 | semidirect |
| 4. #16810984 | C2 | semidirect |
| 5. #16810979 | C2 | semidirect |
| 6. #16810968 | C2 | semidirect |
| 7. #16810629 | C2 | semidirect |
| 8. #16810619 | C2 | semidirect |
| 9. C2×#13133137 | C2 | semidirect |
| 10. #16810581 | C2 | semidirect |
| 11. C53×#417 | C2 | semidirect |
| 15. #13133216 | C22 | semidirect |
| 18. #13133208 | C22 | semidirect |
| 26. #13133141 | C22 | semidirect |
| 27. #13133141 | C22 | semidirect |
| 30. #13133138 | C22 | semidirect |
| 31. #13133138 | C22 | semidirect |
| 34. #13133127 | C22 | semidirect |
| 35. C8×Dic53 | C22 | semidirect |
| 39. #103×C53 | C22 | semidirect |
| 40. #102×C53 | C22 | semidirect |
| 143. #417 | D53 | semidirect |
| 147. C53 | #3136 | semidirect |
| 167. #103 | C2×D53 | semidirect |
| 174. #102 | C2×D53 | semidirect |