Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 10. Q8×Dic53 | C4 | semidirect |
| 17. #13133141 | C4 | semidirect |
| 23. #103×C53 | C4 | semidirect |
| 58. Q8×C53 | C42 | semidirect |
| 117. C53 | #1763 | semidirect |
| 131. #103 | Dic53 | semidirect |
| 168. Q8 | C4×Dic53 | semidirect |