Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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×#13133156 | C2 | semidirect |
| 3. #108×D53 | C2 | semidirect |
| 4. #16810431 | C2 | semidirect |
| 5. #16810430 | C2 | semidirect |
| 6. #16810429 | C2 | semidirect |
| 7. C53×#359 | C2 | semidirect |
| 21. C2×#11719908 | C22 | semidirect |
| 22. #13133153 | C22 | semidirect |
| 25. C2×C16×C53 | C22 | semidirect |
| 26. #108×C53 | C22 | semidirect |
| 115. #359 | D53 | semidirect |
| 116. C53 | #2143 | semidirect |
| 132. C2×C16 | C2×D53 | semidirect |
| 135. #108 | C2×D53 | semidirect |