Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
248 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #16810355 | C2 | semidirect |
| 5. Q8⋊#88322 | C2 | semidirect |
| 6. #16810353 | C2 | semidirect |
| 7. C53×Q8⋊C8 | C2 | semidirect |
| 59. Q8×C53 | M16 | semidirect |
| 79. Dic106 | M16 | semidirect |
| 111. Q8⋊C8 | D53 | semidirect |
| 112. C53 | #1487 | semidirect |
| 167. Q8 | #11719912 | semidirect |