Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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. #16811356 | C2 | semidirect |
| 2. #16811011 | C2 | semidirect |
| 3. #16811007 | C2 | semidirect |
| 4. #16810844 | C2 | semidirect |
| 5. #16810838 | C2 | semidirect |
| 6. #16810817 | C2 | semidirect |
| 7. #16810753 | C2 | semidirect |
| 8. #16810722 | C2 | semidirect |
| 9. C4×D8×C53 | C2 | semidirect |
| 117. C4×D8 | D53 | semidirect |
| 118. C53 | #3403 | semidirect |