Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 161. C53 | #10606 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275703 | 2 |
| #20275491 | 2 |
| #20273468 | 2 |
| #20273399 | 2 |
| C2×#16810368 | 2 |
| #20272589 | 2 |
| C53×#1571 | 2 |
| #10606 | 53 |