Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
680 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 205 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. #16810390 | C2 | direct (N × H) |
| 7. C2×C22⋊Dic53 | C4 | semidirect |
| 10. C23×C4×C53 | C4 | semidirect |
| 13. C2×C22⋊C4×C53 | C4 | semidirect |
| 27. C22×C4×C53 | C2×C4 | semidirect |
| 35. C22⋊Dic53 | C2×C4 | semidirect |
| 100. C2×C53 | #342 | semidirect |
| 106. C53 | C2×#342 | semidirect |
| 109. C23×C4 | Dic53 | semidirect |
| 116. C2×C22⋊C4 | Dic53 | semidirect |
| 133. C22×C4 | C2×Dic53 | semidirect |
| 202. C2 | #16810390 | direct (N × H) |