Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #20272618 | C2 | semidirect |
| 4. #20272573 | C2 | semidirect |
| 156. C53 | #8764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274707 | 2 |
| #20273036 | 2 |
| #20272618 | 2 |
| #20272573 | 2 |
| C53×#2349 | 2 |
| #8764 | 53 |