Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
520 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 129 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. C2×#13133241 | C2 | semidirect |
| 2. #16811268 | C2 | semidirect |
| 3. #16811007 | C2 | semidirect |
| 4. #16810870 | C2 | semidirect |
| 5. #16810838 | C2 | semidirect |
| 6. #16810786 | C2 | semidirect |
| 7. #16810758 | C2 | semidirect |
| 8. #16810702 | C2 | semidirect |
| 9. C4×D8×C53 | C2 | semidirect |
| 11. C2×D4×D53 | C22 | semidirect |
| 13. C2×Dic212 | C22 | semidirect |
| 14. C2×#11719913 | C22 | semidirect |
| 15. C2×#11719923 | C22 | semidirect |
| 18. C2×#11719912 | C22 | semidirect |
| 19. #13133205 | C22 | semidirect |
| 21. #13133197 | C22 | semidirect |
| 27. C4⋊#88322 | C22 | semidirect |
| 28. #13133140 | C22 | semidirect |
| 29. #13133137 | C22 | semidirect |
| 30. #13133129 | C22 | semidirect |
| 32. C4×D4×C53 | C22 | semidirect |
| 33. #107×C53 | C22 | semidirect |
| 34. #102×C53 | C22 | semidirect |
| 35. C4×C8×C53 | C22 | semidirect |
| 51. D8×C53 | D4 | semidirect |
| 132. C4×D8 | D53 | semidirect |
| 134. C53 | #3273 | semidirect |
| 152. C4×D4 | C2×D53 | semidirect |
| 154. #107 | C2×D53 | semidirect |
| 158. #102 | C2×D53 | semidirect |
| 160. C4×C8 | C2×D53 | semidirect |
| 181. D8 | D212 | semidirect |