Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#13133214 | C2 | semidirect |
| 3. #16811013 | C2 | semidirect |
| 4. #16810999 | C2 | semidirect |
| 5. #16810997 | C2 | semidirect |
| 6. C4×#11719917 | C2 | semidirect |
| 7. C53×#532 | C2 | semidirect |
| 11. C2×#11719924 | C22 | semidirect |
| 12. C2×#11719922 | C22 | semidirect |
| 17. #13133128 | C22 | semidirect |
| 18. C4×#88322 | C22 | semidirect |
| 20. C4⋊Q8×C53 | C22 | semidirect |
| 21. #127×C53 | C22 | semidirect |
| 22. #124×C53 | C22 | semidirect |
| 48. #11719917 | D4 | semidirect |
| 71. #88322 | C2×D4 | semidirect |
| 83. C4×C53 | AGL(1,ℤ/8) | semidirect |
| 92. #532 | D53 | semidirect |
| 98. C53 | #3151 | semidirect |
| 106. C4⋊Q8 | C2×D53 | semidirect |
| 110. #127 | C2×D53 | semidirect |
| 111. #124 | C2×D53 | semidirect |
| 174. C4 | #13133242 | semidirect |