Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1094 conjugacy classes of subgroups; only the 319 normal subgroups are shown.
This group has 1094 conjugacy classes of subgroups — too many to draw. Only its 319 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 |
|---|---|---|
| 15. C53×#395 | C4 | semidirect |
| 123. #395 | Dic53 | semidirect |
| 131. C53 | #14655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272986 | 2 |
| #20272983 | 2 |
| #20272977 | 2 |
| #20272947 | 2 |
| C2×C53×#395 | 2 |
| #14655 | 53 |