Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 172. C53 | #10494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275705 | 2 |
| #20273503 | 2 |
| #20273453 | 2 |
| #20273400 | 2 |
| #20273136 | 2 |
| #20272606 | 2 |
| C53×#3229 | 2 |
| #10494 | 53 |