Finite Group DatabasebetaFinite Group DatabasebetaOrder 6784.
800 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 161 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. #16811182 | C2 | semidirect |
| 2. #16810813 | C2 | semidirect |
| 3. #16810810 | C2 | semidirect |
| 4. C2×#13133132 | C2 | semidirect |
| 5. C2×H(5,𝔽2)×C53 | C2 | semidirect |
| 6. C22×C22⋊D53 | C22 | semidirect |
| 8. #13133198 | C22 | semidirect |
| 11. #13133185 | C22 | semidirect |
| 12. C2×C22⋊Dic53 | C22 | semidirect |
| 13. #13133132 | C22 | semidirect |
| 20. C24×C53 | D4 | semidirect |
| 22. C23×D53 | C23 | semidirect |
| 31. C2×D4×C53 | D4 | semidirect |
| 34. C22×C4×C53 | D4 | semidirect |
| 39. C22×Dic53 | C23 | semidirect |
| 42. C22⋊Dic53 | C23 | semidirect |
| 94. C2×H(5,𝔽2) | D53 | semidirect |
| 99. C53 | #3026 | semidirect |
| 115. C24 | C22⋊D53 | semidirect |
| 128. C2×D4 | C22⋊D53 | semidirect |
| 133. C22×C4 | C22⋊D53 | semidirect |