Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #16811333 | C2 | semidirect |
| 2. #16811029 | C2 | semidirect |
| 3. #16811019 | C2 | semidirect |
| 4. #16810923 | C2 | semidirect |
| 5. #16810913 | C2 | semidirect |
| 6. #16810910 | C2 | semidirect |
| 7. #16810900 | C2 | semidirect |
| 8. #16810754 | C2 | semidirect |
| 11. D4×Q8×C53 | C2 | semidirect |
| 62. #11719922 | Q8 | semidirect |
| 92. D212 | C2×Q8 | semidirect |
| 98. #88322 | C2×Q8 | semidirect |
| 123. D4×Q8 | D53 | semidirect |
| 133. C53 | #3384 | semidirect |