Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
792 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 229 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. C22×C8×D53 | C2 | semidirect |
| 3. C2×#13133175 | C2 | semidirect |
| 4. #16810618 | C2 | direct (N × H) |
| 5. C2×#13133141 | C2 | semidirect |
| 6. C2×#13133139 | C2 | semidirect |
| 7. C2×#13133137 | C2 | semidirect |
| 8. C2×#103×C53 | C2 | semidirect |
| 11. C2×#11719949 | C4 | semidirect |
| 19. C2×C8×D53 | C22 | semidirect |
| 21. #13133175 | C22 | semidirect |
| 25. #13133141 | C22 | semidirect |
| 26. #13133139 | C22 | semidirect |
| 27. #13133137 | C22 | semidirect |
| 31. #103×C53 | C22 | semidirect |
| 45. #11719949 | C2×C4 | semidirect |
| 123. C2×C53 | #416 | semidirect |
| 134. C2×#103 | D53 | semidirect |
| 137. C53 | C2×#416 | semidirect |
| 158. #103 | C2×D53 | semidirect |
| 253. C2 | #16810618 | direct (N × H) |