Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 422 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 |
|---|---|---|
| 10. #16811026 | C4 | semidirect |
| 11. #16811019 | C4 | semidirect |
| 167. C53 | #9427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285262 | 2 |
| #20277895 | 2 |
| #20273433 | 2 |
| #20273266 | 2 |
| #20272581 | 2 |
| #20272579 | 2 |
| C53×#1515 | 2 |
| #9427 | 53 |