Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. C22×#11719917 | C2 | semidirect |
| 3. C2×#13133137 | C2 | semidirect |
| 4. #16810385 | C2 | semidirect |
| 5. C53×#380 | C2 | semidirect |
| 12. #13133191 | C4 | semidirect |
| 45. C2×#88322 | D4 | semidirect |
| 108. #380 | D53 | semidirect |
| 110. C53 | #1895 | semidirect |