Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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×#13133243 | C2 | semidirect |
| 2. #16811173 | C2 | semidirect |
| 3. #16810838 | C2 | semidirect |
| 4. #16810828 | C2 | semidirect |
| 5. #16810818 | C2 | semidirect |
| 6. #16810647 | C2 | semidirect |
| 7. #16810622 | C2 | semidirect |
| 8. C2×C4×D4×C53 | C2 | semidirect |
| 14. #13133217 | C22 | semidirect |
| 15. #13133214 | C22 | semidirect |
| 16. #13133205 | C22 | semidirect |
| 21. C4⋊#88322 | C22 | semidirect |
| 22. C4⋊#88322 | C22 | semidirect |
| 23. #13133140 | C22 | semidirect |
| 24. #13133137 | C22 | semidirect |
| 37. C2×D4×C53 | D4 | semidirect |
| 119. C4×C53 | AGL(1,ℤ/8) | semidirect |
| 132. C2×C4×D4 | D53 | semidirect |
| 138. C53 | #3036 | semidirect |
| 174. C2×D4 | D212 | semidirect |
| 250. C4 | #13133243 | semidirect |