Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #16811029 | C2 | semidirect |
| 3. #16810985 | C2 | semidirect |
| 4. #16810958 | C2 | semidirect |
| 6. #16810905 | C2 | semidirect |
| 7. #16810900 | C2 | semidirect |
| 8. #16810680 | C2 | semidirect |
| 9. C2×C4⋊Q8×C53 | C2 | semidirect |
| 113. C2×C4⋊Q8 | D53 | semidirect |
| 122. C53 | #3239 | semidirect |