Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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. #135×D53 | C2 | semidirect |
| 2. #16811056 | C2 | semidirect |
| 3. #16811055 | C2 | semidirect |
| 4. #16811054 | C2 | semidirect |
| 5. #16811053 | C2 | semidirect |
| 6. #16811052 | C2 | semidirect |
| 7. Q32×D53 | C2 | semidirect |
| 8. SD32×D53 | C2 | semidirect |
| 9. D16×D53 | C2 | semidirect |
| 10. C2×C16×D53 | C2 | semidirect |
| 11. C53×#508 | C2 | semidirect |
| 13. #13133240 | C22 | semidirect |
| 14. #13133239 | C22 | semidirect |
| 17. #13133236 | C22 | semidirect |
| 22. Dic424 | C22 | semidirect |
| 23. #13133163 | C22 | semidirect |
| 24. #13133162 | C22 | semidirect |
| 25. #13133161 | C22 | semidirect |
| 26. #13133160 | C22 | semidirect |
| 27. D848 | C22 | semidirect |
| 28. #13133158 | C22 | semidirect |
| 29. C2×#11719908 | C22 | semidirect |
| 32. C16×D53 | C22 | semidirect |
| 33. C16×D53 | C22 | semidirect |
| 34. #135×C53 | C22 | semidirect |
| 35. Q32×C53 | C22 | semidirect |
| 36. SD32×C53 | C22 | semidirect |
| 37. D16×C53 | C22 | semidirect |
| 38. C2×C16×C53 | C22 | semidirect |
| 116. D53 | #508 | direct (N × H) |
| 123. #508 | D53 | direct (N × H) |
| 128. C53 | C2×#508 | semidirect |
| 135. #135 | C2×D53 | semidirect |
| 142. Q32 | C2×D53 | semidirect |
| 146. SD32 | C2×D53 | semidirect |
| 149. D16 | C2×D53 | semidirect |
| 155. C2×C16 | C2×D53 | semidirect |