Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 16. #16810428 | C4 | semidirect |
| 150. C53 | #13154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810440 | 2 |
| #20276436 | 2 |
| #20275586 | 2 |
| #20275468 | 2 |
| #20272821 | 2 |
| #20272814 | 2 |
| C2×C53×#347 | 2 |
| #13154 | 53 |