Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
1112 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 269 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. C22×C22⋊Dic53 | C2 | semidirect |
| 3. C2×#13133131 | C2 | direct (N × H) |
| 4. C22×C22⋊C4×C53 | C2 | semidirect |
| 5. C24×D53 | C4 | semidirect |
| 10. C22×C22⋊D53 | C4 | semidirect |
| 13. C23×Dic53 | C4 | semidirect |
| 15. C2×C22⋊Dic53 | C22 | semidirect |
| 16. #13133131 | C22 | direct (N × H) |
| 20. C2×C22⋊C4×C53 | C22 | semidirect |
| 32. C23×D53 | C2×C4 | semidirect |
| 42. C2×C22⋊D53 | C2×C4 | semidirect |
| 48. C22×Dic53 | C2×C4 | semidirect |
| 50. C22⋊C4×C53 | C23 | semidirect |
| 52. C22⋊Dic53 | C23 | semidirect |
| 77. C22×D53 | C22×C4 | semidirect |
| 88. C2×Dic53 | C22×C4 | semidirect |
| 100. C22×C53 | #99 | semidirect |
| 122. C2×C53 | C2×#99 | semidirect |
| 127. C22×C22⋊C4 | D53 | semidirect |
| 129. C53 | C22×#99 | semidirect |
| 144. C2×C22⋊C4 | C2×D53 | semidirect |
| 177. C22⋊C4 | C22×D53 | semidirect |
| 229. C22 | #13133131 | direct (N × H) |
| 247. C2 | C2×#13133131 | direct (N × H) |