Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
290 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#13133148 | C2 | semidirect |
| 5. #16810385 | C2 | semidirect |
| 6. #16810378 | C2 | semidirect |
| 7. C4×C4⋊C4×C53 | C2 | semidirect |
| 16. #13133137 | C4 | semidirect |
| 123. C4×C4⋊C4 | D53 | semidirect |
| 126. C53 | #1926 | semidirect |