Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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. #16811168 | C2 | semidirect |
| 2. C2×#13133213 | C2 | semidirect |
| 3. #16810998 | C2 | semidirect |
| 4. #16810968 | C2 | semidirect |
| 5. #16810817 | C2 | semidirect |
| 6. #16810816 | C2 | semidirect |
| 7. #16810759 | C2 | semidirect |
| 8. #16810757 | C2 | semidirect |
| 9. #16810756 | C2 | semidirect |
| 10. #16810673 | C2 | semidirect |
| 11. C53×#447 | C2 | semidirect |
| 16. C2×D424 | C22 | semidirect |
| 17. C2×#11719922 | C22 | semidirect |
| 18. C2×#11719922 | C22 | semidirect |
| 19. #13133216 | C22 | semidirect |
| 24. #13133213 | C22 | semidirect |
| 28. D4×Dic53 | C22 | semidirect |
| 29. #13133179 | C22 | semidirect |
| 32. #13133146 | C22 | semidirect |
| 33. #13133139 | C22 | semidirect |
| 34. #13133138 | C22 | semidirect |
| 35. #13133137 | C22 | semidirect |
| 37. C8×Dic53 | C22 | semidirect |
| 39. C2×D8×C53 | C22 | semidirect |
| 41. #102×C53 | C22 | semidirect |
| 117. C2×Dic53 | D8 | semidirect |
| 174. #447 | D53 | semidirect |
| 176. C53 | #3205 | semidirect |
| 185. C2×D8 | C2×D53 | semidirect |
| 204. #102 | C2×D53 | semidirect |