Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
756 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 249 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. #16811390 | C2 | semidirect |
| 3. #16810605 | C2 | semidirect |
| 4. C2×#13133133 | C2 | semidirect |
| 5. C53×#568 | C2 | semidirect |
| 13. C2×#11719917 | C22 | semidirect |
| 14. #13133135 | C22 | semidirect |
| 15. #13133133 | C22 | semidirect |
| 18. C2×M16×C53 | C22 | semidirect |
| 79. #568 | D53 | semidirect |
| 82. C53 | #2888 | semidirect |
| 93. C2×M16 | C2×D53 | semidirect |