Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 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. C2×#13133215 | C2 | semidirect |
| 4. #16810826 | C2 | direct (N × H) |
| 5. C2×#13133146 | C2 | semidirect |
| 6. C2×#13133142 | C2 | semidirect |
| 7. C2×#13133141 | C2 | semidirect |
| 15. #13133215 | C22 | semidirect |
| 23. #13133146 | C22 | semidirect |
| 24. #13133142 | C22 | semidirect |
| 25. #13133141 | C22 | semidirect |
| 88. C2×Dic53 | SD16 | semidirect |
| 111. Dic53 | C2×SD16 | semidirect |
| 114. C2×C53 | #461 | semidirect |
| 126. C53 | C2×#461 | semidirect |
| 231. C2 | #16810826 | direct (N × H) |