Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. C2×#13133242 | C2 | semidirect |
| 2. C22×#11719922 | C2 | semidirect |
| 3. C2×#13133134 | C2 | semidirect |
| 4. C2×#13133133 | C2 | semidirect |
| 5. #16810590 | C2 | semidirect |
| 6. #16810387 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C53 | C2 | semidirect |
| 134. C2×AGL(1,ℤ/8) | D53 | semidirect |
| 140. C53 | #2018 | semidirect |