Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 1. #16811346 | C2 | semidirect |
| 2. #16810985 | C2 | semidirect |
| 3. #16810975 | C2 | semidirect |
| 4. #16810915 | C2 | semidirect |
| 5. #16810900 | C2 | semidirect |
| 7. #16810828 | C2 | semidirect |
| 8. #16810754 | C2 | semidirect |
| 9. #16810723 | C2 | semidirect |
| 11. D4×Q8×C53 | C2 | semidirect |
| 124. D4×Q8 | D53 | semidirect |
| 134. C53 | #3367 | semidirect |