Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 1. C2×#13133240 | C2 | semidirect |
| 2. C2×#13133236 | C2 | semidirect |
| 3. #16811054 | C2 | direct (N × H) |
| 4. C2×#13133163 | C2 | semidirect |
| 5. C2×#13133162 | C2 | semidirect |
| 6. C2×#13133158 | C2 | semidirect |
| 7. C2×C16×D53 | C2 | semidirect |
| 8. C2×SD32×C53 | C2 | semidirect |
| 12. #13133240 | C22 | semidirect |
| 14. #13133236 | C22 | semidirect |
| 20. #13133163 | C22 | semidirect |
| 21. #13133162 | C22 | semidirect |
| 22. #13133158 | C22 | semidirect |
| 24. C16×D53 | C22 | semidirect |
| 27. SD32×C53 | C22 | semidirect |
| 96. C2×C53 | #508 | semidirect |
| 105. C2×SD32 | D53 | semidirect |
| 108. C53 | C2×#508 | semidirect |
| 124. SD32 | C2×D53 | semidirect |
| 197. C2 | #16811054 | direct (N × H) |