Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
416 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 165 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. #16810916 | C2 | direct (N × H) |
| 31. C2×Q8×C53 | Q8 | semidirect |
| 60. Q8×C53 | C2×Q8 | semidirect |
| 94. C2×C53 | #477 | semidirect |
| 106. C53 | C2×#477 | semidirect |
| 131. C2×Q8 | Dic106 | semidirect |
| 159. Q8 | C2×Dic106 | semidirect |
| 191. C2 | #16810916 | direct (N × H) |