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×#13133236 | C2 | semidirect |
| 2. C2×D8×D53 | C2 | semidirect |
| 3. #16811057 | C2 | direct (N × H) |
| 4. C2×#13133162 | C2 | semidirect |
| 5. C2×#13133161 | C2 | semidirect |
| 6. C2×#13133158 | C2 | semidirect |
| 7. C2×#13133156 | C2 | semidirect |
| 8. C2×D16×C53 | C2 | semidirect |
| 12. #13133236 | C22 | semidirect |
| 13. C2×Dic212 | C22 | semidirect |
| 18. D8×D53 | C22 | semidirect |
| 20. #13133162 | C22 | semidirect |
| 21. #13133161 | C22 | semidirect |
| 22. #13133158 | C22 | semidirect |
| 23. #13133156 | C22 | semidirect |
| 24. C2×#11719908 | C22 | semidirect |
| 26. C2×D8×C53 | C22 | semidirect |
| 27. D16×C53 | C22 | semidirect |
| 28. C2×C16×C53 | C22 | semidirect |
| 45. D8×C53 | C23 | semidirect |
| 51. Dic212 | C23 | semidirect |
| 56. C16×C53 | C23 | semidirect |
| 57. #11719908 | C23 | semidirect |
| 100. C2×C53 | #509 | semidirect |
| 110. C2×D16 | D53 | semidirect |
| 112. C53 | C2×#509 | semidirect |
| 124. C2×D8 | C2×D53 | semidirect |
| 129. D16 | C2×D53 | semidirect |
| 132. C2×C16 | C2×D53 | semidirect |
| 155. D8 | C22×D53 | semidirect |
| 161. C16 | C22×D53 | semidirect |
| 205. C2 | #16811057 | direct (N × H) |