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. #16811060 | C2 | semidirect |
| 3. #16811058 | C2 | semidirect |
| 4. #16811056 | C2 | semidirect |
| 5. C2×D848 | C2 | semidirect |
| 6. D16×D53 | C2 | semidirect |
| 7. #16811039 | C2 | semidirect |
| 8. C53×#508 | C2 | semidirect |
| 12. #13133240 | C22 | semidirect |
| 13. C2×D424 | C22 | semidirect |
| 14. D8×D53 | C22 | semidirect |
| 16. #13133160 | C22 | semidirect |
| 17. D848 | C22 | semidirect |
| 18. D848 | C22 | semidirect |
| 19. #13133158 | C22 | semidirect |
| 20. #13133157 | C22 | semidirect |
| 21. #13133156 | C22 | semidirect |
| 22. C16×D53 | C22 | semidirect |
| 23. #135×C53 | C22 | semidirect |
| 24. Q32×C53 | C22 | semidirect |
| 25. SD32×C53 | C22 | semidirect |
| 26. D16×C53 | C22 | semidirect |
| 27. C2×C16×C53 | C22 | semidirect |
| 89. #508 | D53 | semidirect |
| 93. C53 | #3415 | semidirect |
| 98. #135 | C2×D53 | semidirect |
| 102. Q32 | C2×D53 | semidirect |
| 104. SD32 | C2×D53 | semidirect |
| 108. D16 | C2×D53 | semidirect |
| 112. C2×C16 | C2×D53 | semidirect |