Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. #16811157 | C2 | semidirect |
| 2. #16810931 | C2 | semidirect |
| 3. #16810924 | C2 | semidirect |
| 4. #16810864 | C2 | semidirect |
| 6. #16810852 | C2 | semidirect |
| 7. #16810846 | C2 | semidirect |
| 8. #16810839 | C2 | semidirect |
| 9. C2×C4⋊C8×C53 | C2 | semidirect |
| 115. C2×C4⋊C8 | D53 | semidirect |
| 116. C53 | #3250 | semidirect |