Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
794 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13133198 | C2 | semidirect |
| 2. #16810813 | C2 | direct (N × H) |
| 3. C2×#13133132 | C2 | semidirect |
| 5. C23×Dic53 | C22 | semidirect |
| 7. #13133198 | C22 | semidirect |
| 10. C2×C22⋊Dic53 | C22 | semidirect |
| 11. #13133132 | C22 | semidirect |
| 35. C22×Dic53 | C23 | semidirect |
| 38. C22⋊Dic53 | C23 | semidirect |
| 81. C2×C53 | #458 | semidirect |
| 87. C53 | C2×#458 | semidirect |
| 163. C2 | #16810813 | direct (N × H) |