Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 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. #16810823 | C2 | semidirect |
| 4. #16810818 | C2 | semidirect |
| 5. #16810647 | C2 | semidirect |
| 6. #16810627 | C2 | semidirect |
| 7. C4×#41×C53 | C2 | semidirect |
| 11. C2×#11719924 | C22 | semidirect |
| 12. C2×#11719922 | C22 | semidirect |
| 17. C4⋊#88322 | C22 | semidirect |
| 18. #13133137 | C22 | semidirect |
| 20. C4×Q8×C53 | C22 | semidirect |
| 22. C4×D4×C53 | C22 | semidirect |
| 29. #41×C53 | D4 | semidirect |
| 63. Q8×C53 | C2×D4 | semidirect |
| 66. D4×C53 | C2×D4 | semidirect |
| 96. C4×C53 | AGL(1,ℤ/8) | semidirect |
| 107. C4×#41 | D53 | semidirect |
| 112. C53 | #3038 | semidirect |
| 123. C4×Q8 | C2×D53 | semidirect |
| 125. C4×D4 | C2×D53 | semidirect |
| 134. #41 | D212 | semidirect |
| 168. Q8 | C2×D212 | semidirect |
| 176. D4 | C2×D212 | semidirect |
| 201. C4 | #13133242 | semidirect |