Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic424 | C2 | semidirect |
| 3. C2×#13133162 | C2 | semidirect |
| 4. #16810864 | C2 | semidirect |
| 5. #16810428 | C2 | semidirect |
| 6. #16810425 | C2 | semidirect |
| 7. C53×C22⋊C16 | C2 | semidirect |
| 92. C22⋊C16 | D53 | semidirect |
| 93. C53 | #2189 | semidirect |