Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2878 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 2878 conjugacy classes of subgroups — too many to draw. Only its 491 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. #20272952 | C2 | semidirect |
| 5. C22×C4×Dic53 | C22 | semidirect |
| 6. #16810479 | C4 | semidirect |
| 7. C2×#13133124 | C22 | semidirect |
| 10. C53×#379 | C4 | semidirect |
| 29. C24×C53 | C42 | semidirect |
| 87. #379 | Dic53 | semidirect |
| 89. C53 | #13827 | semidirect |
| 108. C24 | C4×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810479 | 2 |
| #20272952 | 2 |
| C2×C53×#379 | 2 |
| #13827 | 53 |