Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
408 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 129 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. #16811173 | C2 | semidirect |
| 2. #16811157 | C2 | semidirect |
| 3. #16811032 | C2 | semidirect |
| 4. #16811012 | C2 | semidirect |
| 5. #16810988 | C2 | semidirect |
| 6. #16810983 | C2 | semidirect |
| 7. #16810876 | C2 | semidirect |
| 8. #16810869 | C2 | semidirect |
| 9. C4×#11719913 | C2 | semidirect |
| 10. C4×D424 | C2 | semidirect |
| 11. C4×M16×C53 | C2 | semidirect |
| 110. C8×C53 | #41 | semidirect |
| 148. C4×M16 | D53 | semidirect |
| 149. C53 | #3171 | semidirect |
| 248. C8 | #11719945 | semidirect |