Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #16811025 | C2 | semidirect |
| 3. #16811007 | C2 | semidirect |
| 4. #16810978 | C2 | semidirect |
| 5. #16810881 | C2 | semidirect |
| 7. #16810869 | C2 | semidirect |
| 8. #16810736 | C2 | semidirect |
| 9. #16810731 | C2 | semidirect |
| 10. #16810725 | C2 | semidirect |
| 11. C4×M16×C53 | C2 | semidirect |
| 120. C4×M16 | D53 | semidirect |
| 121. C53 | #3183 | semidirect |