Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13133250 | C2 | semidirect |
| 3. C2×#13133204 | C2 | semidirect |
| 4. #16810803 | C2 | direct (N × H) |
| 5. C2×#13133143 | C2 | semidirect |
| 6. C2×#100×C53 | C2 | semidirect |
| 12. C22×Dic106 | C22 | semidirect |
| 16. #13133250 | C22 | semidirect |
| 20. #13133204 | C22 | semidirect |
| 22. C2×C4×Dic53 | C22 | semidirect |
| 23. #13133143 | C22 | semidirect |
| 25. C2×M16×C53 | C22 | semidirect |
| 26. #100×C53 | C22 | semidirect |
| 55. C2×Dic106 | C23 | semidirect |
| 57. M16×C53 | C23 | semidirect |
| 61. C4×Dic53 | C23 | semidirect |
| 117. C2×C53 | #455 | semidirect |
| 125. C2×#100 | D53 | semidirect |
| 126. C53 | C2×#455 | semidirect |
| 140. C2×M16 | C2×D53 | semidirect |
| 146. #100 | C2×D53 | semidirect |
| 179. M16 | C22×D53 | semidirect |
| 237. C2 | #16810803 | direct (N × H) |