Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
350 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 107 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. #16810750 | C4 | semidirect |
| 12. #16810747 | C4 | semidirect |
| 176. C53 | #8679 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283645 | 2 |
| #20274845 | 2 |
| #20273461 | 2 |
| #20273280 | 2 |
| #20273278 | 2 |
| #20272575 | 2 |
| C53×#1286 | 2 |
| #8679 | 53 |