Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
424 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×Q8×Dic53 | C2 | semidirect |
| 3. #16810937 | C2 | semidirect |
| 4. #16810934 | C2 | semidirect |
| 5. #16810916 | C2 | semidirect |
| 6. #16810821 | C2 | semidirect |
| 7. #16810762 | C2 | semidirect |
| 8. #16810726 | C2 | semidirect |
| 9. #16810724 | C2 | semidirect |
| 10. #16810677 | C2 | semidirect |
| 11. C53×#448 | C2 | semidirect |
| 87. Q8×C53 | #41 | semidirect |
| 148. #448 | D53 | semidirect |
| 152. C53 | #3112 | semidirect |
| 229. Q8 | #11719947 | semidirect |