Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
282 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 67 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. #16811251 | C2 | semidirect |
| 5. #16810391 | C2 | semidirect |
| 6. #16810383 | C2 | semidirect |
| 7. C53×#339 | C2 | semidirect |
| 34. C2×D212 | Q8 | semidirect |
| 119. #339 | D53 | semidirect |
| 120. C53 | #2027 | semidirect |