Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 214. C53 | #13431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285606 | 2 |
| #20276410 | 2 |
| #20276409 | 2 |
| #20275267 | 2 |
| #20274935 | 2 |
| #20272837 | 2 |
| C53×#1915 | 2 |
| #13431 | 53 |