Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. #16810936 | C2 | direct (N × H) |
| 3. C2×#13133150 | C2 | semidirect |
| 4. C2×#13133137 | C2 | semidirect |
| 5. C2×C22⋊#88322 | C2 | semidirect |
| 6. C22×C4⋊C4×C53 | C2 | semidirect |
| 14. #13133150 | C22 | semidirect |
| 15. #13133137 | C22 | semidirect |
| 16. C22⋊#88322 | C22 | semidirect |
| 22. C2×C4⋊C4×C53 | C22 | semidirect |
| 91. C2×C53 | #480 | semidirect |
| 97. C22×C4⋊C4 | D53 | semidirect |
| 102. C53 | C2×#480 | semidirect |
| 114. C2×C4⋊C4 | C2×D53 | semidirect |
| 187. C2 | #16810936 | direct (N × H) |