Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
338 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 22. C2×Dic212 | C4 | semidirect |
| 23. C2×#11719925 | C4 | semidirect |
| 24. C2×#11719925 | C4 | semidirect |
| 28. C2×Q16×C53 | C4 | semidirect |
| 81. C2×#6157 | Q16 | semidirect |
| 145. C53 | #1878 | semidirect |
| 153. C2×Q16 | #6157 | semidirect |