Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
312 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. #16811627 | C2 | semidirect |
| 3. C4×C4⋊#6157 | C2 | semidirect |
| 4. #16811493 | C2 | semidirect |
| 14. C4×Dic106 | C4 | semidirect |
| 15. #13133182 | C4 | semidirect |
| 16. D4×Dic53 | C4 | semidirect |
| 23. C4×D4×C53 | C4 | semidirect |
| 64. D4×C53 | C4⋊C4 | semidirect |
| 87. Dic106 | C4⋊C4 | semidirect |
| 100. C4×C53 | #104 | semidirect |
| 121. C53 | #1806 | semidirect |
| 129. C4×D4 | #6157 | semidirect |
| 181. D4 | C4⋊#6157 | semidirect |
| 222. C4 | #13133281 | semidirect |