Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
5294 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 5294 conjugacy classes of subgroups — too many to draw. Only its 827 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. C22×#13133198 | C2 | semidirect |
| 2. C2×#16810813 | C2 | direct (N × H) |
| 3. C22×#13133132 | C2 | semidirect |
| 5. C24×Dic53 | C22 | semidirect |
| 7. C2×#13133198 | C22 | semidirect |
| 10. C22×C22⋊Dic53 | C22 | semidirect |
| 11. #16810813 | C22 | direct (N × H) |
| 12. C2×#13133132 | C22 | semidirect |
| 21. C23×Dic53 | C23 | semidirect |
| 23. #13133198 | C23 | semidirect |
| 27. C2×C22⋊Dic53 | C23 | semidirect |
| 28. #13133132 | C23 | semidirect |
| 80. C22×Dic53 | C24 | semidirect |
| 83. C22⋊Dic53 | C24 | semidirect |
| 126. C22×C53 | #458 | semidirect |
| 140. C2×C53 | C2×#458 | semidirect |
| 155. C53 | C22×#458 | semidirect |
| 263. C22 | #16810813 | direct (N × H) |
| 273. C2 | C2×#16810813 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133198 | 2 |
| C2×#16810813 | 2 |
| C22×#13133132 | 2 |
| C22×H(5,𝔽2)×C53 | 2 |
| C22×#458 | 53 |