Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#13133240 | C2 | semidirect |
| 2. C2×D8×D53 | C2 | semidirect |
| 3. #16811060 | C2 | direct (N × H) |
| 4. C2×#13133160 | C2 | semidirect |
| 5. C2×D848 | C2 | semidirect |
| 6. C2×#13133158 | C2 | semidirect |
| 7. C2×#13133156 | C2 | semidirect |
| 8. C2×SD32×C53 | C2 | semidirect |
| 12. #13133240 | C22 | semidirect |
| 15. C2×D424 | C22 | semidirect |
| 18. D8×D53 | C22 | semidirect |
| 20. #13133160 | C22 | semidirect |
| 21. D848 | C22 | semidirect |
| 22. #13133158 | C22 | semidirect |
| 23. #13133156 | C22 | semidirect |
| 24. C2×#11719908 | C22 | semidirect |
| 25. C2×Q16×C53 | C22 | semidirect |
| 27. SD32×C53 | C22 | semidirect |
| 28. C2×C16×C53 | C22 | semidirect |
| 43. Q16×C53 | C23 | semidirect |
| 53. D424 | C23 | semidirect |
| 56. C16×C53 | C23 | semidirect |
| 57. #11719908 | C23 | semidirect |
| 99. C2×C53 | #509 | semidirect |
| 108. C2×SD32 | D53 | semidirect |
| 112. C53 | C2×#509 | semidirect |
| 117. C2×Q16 | C2×D53 | semidirect |
| 127. SD32 | C2×D53 | semidirect |
| 132. C2×C16 | C2×D53 | semidirect |
| 147. Q16 | C22×D53 | semidirect |
| 161. C16 | C22×D53 | semidirect |
| 205. C2 | #16811060 | direct (N × H) |