Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#11719945 | C2 | semidirect |
| 2. C22×#11719913 | C2 | semidirect |
| 3. C22×D424 | C2 | semidirect |
| 4. C2×#13133191 | C2 | semidirect |
| 5. #16810770 | C2 | direct (N × H) |
| 6. C2×#13133142 | C2 | semidirect |
| 7. C2×#13133139 | C2 | semidirect |
| 8. C2×C22⋊C8×C53 | C2 | semidirect |
| 12. C2×#11719945 | C22 | semidirect |
| 20. C2×#11719913 | C22 | semidirect |
| 22. C2×D424 | C22 | semidirect |
| 24. #13133191 | C22 | semidirect |
| 27. #13133142 | C22 | semidirect |
| 28. #13133139 | C22 | semidirect |
| 32. C22⋊C8×C53 | C22 | semidirect |
| 56. C2×D212 | D4 | semidirect |
| 63. C2×Dic106 | D4 | semidirect |
| 107. D212 | C2×D4 | semidirect |
| 111. Dic106 | C2×D4 | semidirect |
| 138. C2×C53 | #449 | semidirect |
| 151. C2×C22⋊C8 | D53 | semidirect |
| 152. C53 | C2×#449 | semidirect |
| 176. C22⋊C8 | C2×D53 | semidirect |
| 283. C2 | #16810770 | direct (N × H) |