Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13133239 | C2 | semidirect |
| 2. #16811053 | C2 | direct (N × H) |
| 3. C2×#13133163 | C2 | semidirect |
| 4. C2×#13133161 | C2 | semidirect |
| 5. C2×#13133160 | C2 | semidirect |
| 6. C2×#13133158 | C2 | semidirect |
| 7. C22×#11719908 | C2 | semidirect |
| 8. C2×#135×C53 | C2 | semidirect |
| 11. #13133239 | C22 | semidirect |
| 15. #13133163 | C22 | semidirect |
| 16. #13133161 | C22 | semidirect |
| 17. #13133160 | C22 | semidirect |
| 18. #13133158 | C22 | semidirect |
| 21. C2×#11719908 | C22 | semidirect |
| 24. #135×C53 | C22 | semidirect |
| 97. C2×C53 | #508 | semidirect |
| 101. C2×#135 | D53 | semidirect |
| 108. C53 | C2×#508 | semidirect |
| 114. #135 | C2×D53 | semidirect |
| 197. C2 | #16811053 | direct (N × H) |