Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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×Q16×D53 | C2 | semidirect |
| 3. #16811062 | C2 | direct (N × H) |
| 4. C2×Dic424 | C2 | semidirect |
| 5. C2×#13133163 | C2 | semidirect |
| 6. C2×#13133161 | C2 | semidirect |
| 7. C2×#13133156 | C2 | semidirect |
| 8. C2×SD32×C53 | C2 | semidirect |
| 17. Q16×D53 | C22 | semidirect |
| 20. Dic424 | C22 | semidirect |
| 21. #13133163 | C22 | semidirect |
| 22. #13133161 | C22 | semidirect |
| 23. #13133156 | C22 | semidirect |
| 27. SD32×C53 | C22 | semidirect |
| 95. C2×C53 | #510 | semidirect |
| 104. C2×SD32 | D53 | semidirect |
| 106. C53 | C2×#510 | semidirect |
| 123. SD32 | C2×D53 | semidirect |
| 193. C2 | #16811062 | direct (N × H) |