Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. C2×C8×Dic53 | C2 | semidirect |
| 5. #16810378 | C2 | semidirect |
| 6. #16810377 | C2 | semidirect |
| 7. C2×C4×C8×C53 | C2 | semidirect |
| 13. C2×C8×D53 | C4 | semidirect |
| 16. #13133129 | C4 | semidirect |
| 42. #11719921 | C8 | direct (N × H) |
| 60. C2×C4×C53 | C2×C8 | semidirect |
| 72. C2×Dic53 | C2×C8 | semidirect |
| 78. C8×C53 | C22⋊C4 | semidirect |
| 90. C2×D53 | C4×C8 | semidirect |
| 108. C2×C4×C8 | D53 | semidirect |
| 112. C53 | C8×C22⋊C4 | semidirect |
| 175. C2×C4 | C8×D53 | semidirect |
| 185. C8 | #11719921 | direct (N × H) |