Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
528 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 528 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 |
|---|---|---|
| 1. C2×#13133216 | C2 | semidirect |
| 3. #16810968 | C2 | direct (N × H) |
| 4. C2×#13133139 | C2 | semidirect |
| 5. C2×#13133138 | C2 | semidirect |
| 6. C2×#13133137 | C2 | semidirect |
| 7. C2×C8×Dic53 | C2 | semidirect |
| 8. C2×#102×C53 | C2 | semidirect |
| 15. #13133216 | C22 | semidirect |
| 21. #13133139 | C22 | semidirect |
| 22. #13133138 | C22 | semidirect |
| 23. #13133137 | C22 | semidirect |
| 24. C8×Dic53 | C22 | semidirect |
| 28. #102×C53 | C22 | semidirect |
| 114. C2×C53 | #486 | semidirect |
| 125. C2×#102 | D53 | semidirect |
| 127. C53 | C2×#486 | semidirect |
| 146. #102 | C2×D53 | semidirect |
| 233. C2 | #16810968 | direct (N × H) |