Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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×#13133158 | C2 | semidirect |
| 2. C2×#13133157 | C2 | semidirect |
| 3. #16810859 | C2 | semidirect |
| 4. #16810450 | C2 | semidirect |
| 5. #16810424 | C2 | semidirect |
| 6. #16810423 | C2 | semidirect |
| 7. C53×#466 | C2 | semidirect |
| 39. #11719908 | D4 | semidirect |
| 83. #466 | D53 | semidirect |
| 87. C53 | #2218 | semidirect |