Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
402 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 115 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×#13133141 | C2 | semidirect |
| 4. #16810530 | C2 | semidirect |
| 5. #16810386 | C2 | semidirect |
| 6. #16810377 | C2 | semidirect |
| 24. C2×SD16×C53 | C4 | semidirect |
| 32. C2×Q8×C53 | C2×C4 | semidirect |
| 51. C2×C8×C53 | C2×C4 | semidirect |
| 99. C2×Dic53 | SD16 | semidirect |
| 141. C53 | #1877 | semidirect |
| 147. C2×SD16 | Dic53 | semidirect |
| 166. C2×Q8 | C2×Dic53 | semidirect |
| 188. C2×C8 | C2×Dic53 | semidirect |