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 |
|---|---|---|
| 2. C2×#13133152 | C2 | semidirect |
| 3. C2×#13133137 | C2 | semidirect |
| 4. C2×#13133133 | C2 | semidirect |
| 5. #16810590 | C2 | semidirect |
| 6. #16810392 | C2 | semidirect |
| 7. C53×#417 | C2 | semidirect |
| 119. #417 | D53 | semidirect |
| 124. C53 | #2051 | semidirect |