Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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×#13133242 | C2 | semidirect |
| 2. C2×#13133242 | C2 | semidirect |
| 3. #16811390 | C2 | semidirect |
| 4. #16810891 | C2 | semidirect |
| 5. #16810888 | C2 | semidirect |
| 6. #16810671 | C2 | semidirect |
| 7. #16810607 | C2 | semidirect |
| 8. C2×#13133133 | C2 | semidirect |
| 9. C53×#575 | C2 | semidirect |
| 16. C2×#11719924 | C22 | semidirect |
| 18. C2×#11719922 | C22 | semidirect |
| 20. #13133224 | C22 | semidirect |
| 25. #13133152 | C22 | semidirect |
| 26. #13133136 | C22 | semidirect |
| 27. #13133134 | C22 | semidirect |
| 28. #13133133 | C22 | semidirect |
| 32. #137×C53 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C53 | C22 | semidirect |
| 148. #575 | D53 | semidirect |
| 157. C53 | #3068 | semidirect |
| 162. #137 | C2×D53 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D53 | semidirect |