Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
348 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 45. Q8×C53 | Q16 | semidirect |
| 77. C53 | #3395 | semidirect |
| 117. Q8 | #11719925 | semidirect |