Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16811134 | C2 | semidirect |
| 2. #16810965 | C2 | semidirect |
| 3. #16810948 | C2 | semidirect |
| 4. #16810864 | C2 | semidirect |
| 5. #16810859 | C2 | semidirect |
| 6. #16810852 | C2 | semidirect |
| 7. #16810787 | C2 | semidirect |
| 8. #16810770 | C2 | semidirect |
| 9. C2×C22⋊C8×C53 | C2 | semidirect |
| 11. C2×Dic212 | C22 | semidirect |
| 12. C2×#11719913 | C22 | semidirect |
| 13. C2×D424 | C22 | semidirect |
| 23. #13133151 | C22 | semidirect |
| 24. #13133151 | C22 | semidirect |
| 25. #13133149 | C22 | semidirect |
| 26. #13133142 | C22 | semidirect |
| 27. #13133142 | C22 | semidirect |
| 28. #13133139 | C22 | semidirect |
| 29. #13133139 | C22 | semidirect |
| 130. C2×C22⋊C8 | D53 | semidirect |
| 131. C53 | #3191 | semidirect |