Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
450 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 450 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. #16811159 | C2 | semidirect |
| 2. C2×D4×Dic53 | C2 | semidirect |
| 3. #16810951 | C2 | semidirect |
| 4. #16810937 | C2 | semidirect |
| 5. #16810921 | C2 | semidirect |
| 6. #16810840 | C2 | semidirect |
| 8. #16810732 | C2 | semidirect |
| 9. #16810724 | C2 | semidirect |
| 10. #16810677 | C2 | semidirect |
| 11. C53×#450 | C2 | semidirect |
| 15. #13133208 | C22 | semidirect |
| 16. #13133206 | C22 | semidirect |
| 19. Q8×Dic53 | C22 | semidirect |
| 24. #13133179 | C22 | semidirect |
| 30. #13133151 | C22 | semidirect |
| 31. #13133148 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133141 | C22 | semidirect |
| 34. #13133139 | C22 | semidirect |
| 37. #13133127 | C22 | semidirect |
| 147. #450 | D53 | semidirect |
| 152. C53 | #3114 | semidirect |