Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 99 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×#13133142 | C2 | semidirect |
| 4. C2×#13133140 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C53×#340 | C2 | semidirect |
| 15. #13133197 | C4 | semidirect |
| 138. #340 | D53 | semidirect |
| 139. C53 | #1894 | semidirect |