Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16811425 | C2 | semidirect |
| 2. #16811424 | C2 | semidirect |
| 3. #16811061 | C2 | semidirect |
| 4. #16811060 | C2 | semidirect |
| 5. #16811057 | C2 | semidirect |
| 6. #16811054 | C2 | semidirect |
| 7. #16811053 | C2 | semidirect |
| 8. C2×#13133158 | C2 | semidirect |
| 9. D16×D53 | C2 | semidirect |
| 10. #16811041 | C2 | semidirect |
| 11. C53×#509 | C2 | semidirect |
| 18. #13133240 | C22 | semidirect |
| 19. #13133239 | C22 | semidirect |
| 20. #13133236 | C22 | semidirect |
| 21. C2×D424 | C22 | semidirect |
| 22. D8×D53 | C22 | semidirect |
| 23. D8×D53 | C22 | semidirect |
| 25. #13133163 | C22 | semidirect |
| 26. #13133162 | C22 | semidirect |
| 27. #13133161 | C22 | semidirect |
| 28. #13133160 | C22 | semidirect |
| 29. D848 | C22 | semidirect |
| 30. #13133158 | C22 | semidirect |
| 31. #13133158 | C22 | semidirect |
| 32. #13133158 | C22 | semidirect |
| 33. #13133156 | C22 | semidirect |
| 34. C2×#11719908 | C22 | semidirect |
| 35. C16×D53 | C22 | semidirect |
| 36. #135×C53 | C22 | semidirect |
| 37. C2×D8×C53 | C22 | semidirect |
| 38. SD32×C53 | C22 | semidirect |
| 39. D16×C53 | C22 | semidirect |
| 40. M32×C53 | C22 | semidirect |
| 135. #509 | D53 | semidirect |
| 141. C53 | #3415 | semidirect |
| 151. #135 | C2×D53 | semidirect |
| 155. C2×D8 | C2×D53 | semidirect |
| 161. SD32 | C2×D53 | semidirect |
| 166. D16 | C2×D53 | semidirect |
| 168. M32 | C2×D53 | semidirect |