Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
296 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 138. C53 | #10669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275695 | 2 |
| #20274834 | 2 |
| #20273491 | 2 |
| #20273119 | 2 |
| #20273117 | 2 |
| #20272543 | 2 |
| C53×#1570 | 2 |
| #10669 | 53 |