Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
334 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 97 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. #16810632 | C2 | semidirect |
| 4. #16810530 | C2 | semidirect |
| 5. #16810391 | C2 | semidirect |
| 6. #16810384 | C2 | semidirect |
| 24. #137×C53 | C4 | semidirect |
| 37. C2×Q8×C53 | C2×C4 | semidirect |
| 50. M16×C53 | C2×C4 | semidirect |
| 132. C53 | #1882 | semidirect |
| 136. #137 | Dic53 | semidirect |
| 162. C2×Q8 | C2×Dic53 | semidirect |
| 177. M16 | C2×Dic53 | semidirect |