Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
564 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13133206 | C2 | semidirect |
| 3. C2×D4×Dic53 | C2 | semidirect |
| 4. #16810840 | C2 | direct (N × H) |
| 5. C2×#13133146 | C2 | semidirect |
| 6. C2×#13133141 | C2 | semidirect |
| 7. C2×#13133139 | C2 | semidirect |
| 8. C22×SD16×C53 | C2 | semidirect |
| 15. #13133206 | C22 | semidirect |
| 17. D4×Dic53 | C22 | semidirect |
| 23. #13133146 | C22 | semidirect |
| 24. #13133141 | C22 | semidirect |
| 25. #13133139 | C22 | semidirect |
| 29. C2×SD16×C53 | C22 | semidirect |
| 119. C2×C53 | #463 | semidirect |
| 124. C22×SD16 | D53 | semidirect |
| 132. C53 | C2×#463 | semidirect |
| 138. C2×SD16 | C2×D53 | semidirect |
| 243. C2 | #16810840 | direct (N × H) |