Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
320 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. M16×Dic53 | C2 | semidirect |
| 4. #16810469 | C2 | semidirect |
| 5. #16810384 | C2 | semidirect |
| 6. #16810383 | C2 | semidirect |
| 9. Q8×Dic53 | C4 | semidirect |
| 11. D4×Dic53 | C4 | semidirect |
| 17. #13133144 | C4 | semidirect |
| 24. #104×C53 | C4 | semidirect |
| 39. M16×C53 | C2×C4 | semidirect |
| 42. C42×C53 | C2×C4 | semidirect |
| 51. C4×Dic53 | C2×C4 | semidirect |
| 55. #11719917 | C2×C4 | semidirect |
| 114. C53 | #1759 | semidirect |
| 128. #104 | Dic53 | semidirect |
| 148. M16 | C2×Dic53 | semidirect |
| 163. C42 | C2×Dic53 | semidirect |