Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
752 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 309 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 | direct (N × H) |
| 4. C2×#13133141 | C2 | semidirect |
| 14. #13133141 | C22 | semidirect |
| 18. C22×Q8×C53 | C4 | semidirect |
| 31. C2×Q8×C53 | C2×C4 | semidirect |
| 87. C2×C53 | #419 | semidirect |
| 95. C53 | C2×#419 | semidirect |
| 99. C22×Q8 | Dic53 | semidirect |
| 121. C2×Q8 | C2×Dic53 | semidirect |
| 176. C2 | #16810632 | direct (N × H) |