Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
300 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 3. #16810578 | C2 | semidirect |
| 4. C2×C8×Dic53 | C2 | semidirect |
| 5. #16810387 | C2 | semidirect |
| 6. #16810384 | C2 | semidirect |
| 12. #13133144 | C4 | semidirect |
| 13. #13133141 | C4 | semidirect |
| 14. #13133138 | C4 | semidirect |
| 20. #131×C53 | C4 | semidirect |
| 106. C53 | #1764 | semidirect |
| 109. #131 | Dic53 | semidirect |