Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
398 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 125 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. #16810923 | C2 | semidirect |
| 3. #16810915 | C2 | semidirect |
| 4. #16810910 | C2 | semidirect |
| 5. #16810857 | C2 | semidirect |
| 6. #16810850 | C2 | semidirect |
| 7. #16810838 | C2 | semidirect |
| 8. #16810820 | C2 | semidirect |
| 9. #16810815 | C2 | semidirect |
| 10. C2×C4⋊#88322 | C2 | semidirect |
| 11. C53×#532 | C2 | semidirect |
| 142. #532 | D53 | semidirect |
| 153. C53 | #3247 | semidirect |