Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1354 conjugacy classes of subgroups; only the 327 normal subgroups are shown.
This group has 1354 conjugacy classes of subgroups — too many to draw. Only its 327 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. #20272986 | C2 | semidirect |
| 4. #20272940 | C2 | semidirect |
| 15. C53×#393 | C4 | semidirect |
| 143. #393 | Dic53 | semidirect |
| 149. C53 | #14609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272986 | 2 |
| #20272964 | 2 |
| #20272952 | 2 |
| #20272940 | 2 |
| C2×C53×#393 | 2 |
| #14609 | 53 |