Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #16811002 | C2 | semidirect |
| 5. #16810833 | C2 | semidirect |
| 6. #16810830 | C2 | semidirect |
| 8. #16810754 | C2 | semidirect |
| 9. #16810728 | C2 | semidirect |
| 11. C53×#557 | C2 | semidirect |
| 120. #557 | D53 | semidirect |
| 131. C53 | #3398 | semidirect |