Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
368 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13133148 | C2 | semidirect |
| 3. C2×#13133137 | C2 | semidirect |
| 4. C2×#13133137 | C2 | semidirect |
| 5. C2×C22⋊#88322 | C2 | semidirect |
| 6. #16810385 | C2 | semidirect |
| 7. C53×#380 | C2 | semidirect |
| 60. C2×#88322 | D4 | semidirect |
| 149. #380 | D53 | semidirect |
| 151. C53 | #2034 | semidirect |