Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 232. C53 | #10563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275184 | 2 |
| #20275149 | 2 |
| #20274919 | 2 |
| #20273287 | 2 |
| #20273079 | 2 |
| #20272620 | 2 |
| C53×#3195 | 2 |
| #10563 | 53 |