Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
280 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 141 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. Q8⋊#88322 | C2 | direct (N × H) |
| 22. C2×Q8×C53 | C8 | semidirect |
| 46. Q8×C53 | C2×C8 | semidirect |
| 79. C2×C53 | Q8⋊C8 | semidirect |
| 87. C53 | C2×Q8⋊C8 | semidirect |
| 105. C2×Q8 | #88322 | semidirect |
| 129. Q8 | C2×#88322 | semidirect |
| 161. C2 | Q8⋊#88322 | direct (N × H) |