Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
514 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20273396 | C2 | semidirect |
| 4. #20272618 | C2 | semidirect |
| 151. C53 | #9399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283756 | 2 |
| #20274707 | 2 |
| #20273396 | 2 |
| #20272618 | 2 |
| C53×#2563 | 2 |
| #9399 | 53 |