Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
| 29. Q8×D53 | C8 | semidirect |
| 60. Q8×C53 | C2×C8 | semidirect |
| 80. Dic106 | C2×C8 | semidirect |
| 105. D53 | Q8⋊C8 | direct (N × H) |
| 112. Q8⋊C8 | D53 | direct (N × H) |
| 113. C53 | C2×Q8⋊C8 | semidirect |
| 169. Q8 | C8×D53 | semidirect |