Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
648 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×D424 | C2 | semidirect |
| 2. C22×#11719922 | C2 | semidirect |
| 3. C2×#13133213 | C2 | semidirect |
| 4. C2×#13133179 | C2 | semidirect |
| 5. #16810817 | C2 | direct (N × H) |
| 6. C2×#13133146 | C2 | semidirect |
| 7. C2×#13133137 | C2 | semidirect |
| 8. C2×#102×C53 | C2 | semidirect |
| 15. C2×D424 | C22 | semidirect |
| 17. C2×#11719922 | C22 | semidirect |
| 20. #13133213 | C22 | semidirect |
| 22. #13133179 | C22 | semidirect |
| 25. #13133146 | C22 | semidirect |
| 26. #13133137 | C22 | semidirect |
| 30. #102×C53 | C22 | semidirect |
| 51. C2×D212 | D4 | semidirect |
| 92. C2×Dic53 | D8 | semidirect |
| 100. D212 | C2×D4 | semidirect |
| 125. Dic53 | C2×D8 | semidirect |
| 128. C2×C53 | #459 | semidirect |
| 141. C2×#102 | D53 | semidirect |
| 142. C53 | C2×#459 | semidirect |
| 164. #102 | C2×D53 | semidirect |
| 263. C2 | #16810817 | direct (N × H) |