Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
256 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 53 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×#13133162 | C2 | semidirect |
| 3. C2×#13133161 | C2 | semidirect |
| 4. #16810865 | C2 | semidirect |
| 5. #16810423 | C2 | semidirect |
| 6. #16810402 | C2 | semidirect |
| 7. C53×#357 | C2 | semidirect |
| 9. C2×Dic212 | C22 | semidirect |
| 18. C2×#11719908 | C22 | semidirect |
| 21. C2×C16×C53 | C22 | semidirect |
| 22. #107×C53 | C22 | semidirect |
| 79. C2×D53 | SD32 | semidirect |
| 97. #357 | D53 | semidirect |
| 99. C53 | #2187 | semidirect |
| 112. C2×C16 | C2×D53 | semidirect |
| 113. #107 | C2×D53 | semidirect |