Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #16810680 | C2 | semidirect |
| 3. #16810359 | C2 | semidirect |
| 5. C4×C4⋊C4×C53 | C2 | semidirect |
| 7. #13133209 | C4 | semidirect |
| 8. #13133205 | C4 | semidirect |
| 12. C4×Dic106 | C4 | semidirect |
| 13. C4×D212 | C4 | semidirect |
| 101. C4×C4⋊C4 | D53 | semidirect |
| 104. C53 | #1509 | semidirect |