Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#13133141 | C2 | semidirect |
| 5. #16810386 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C2×#103×C53 | C2 | semidirect |
| 12. #13133193 | C4 | semidirect |
| 32. C2×Q8×C53 | C2×C4 | semidirect |
| 56. C4⋊Dic53 | C2×C4 | semidirect |
| 116. C2×D53 | #103 | semidirect |
| 138. C2×#103 | D53 | semidirect |
| 142. C53 | #1872 | semidirect |
| 167. C2×Q8 | C4×D53 | semidirect |