Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 12. #16810919 | C4 | semidirect |
| 13. #16810834 | C4 | semidirect |
| 117. C4×Dic53 | Q16 | semidirect |
| 210. C53 | #9232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284755 | 2 |
| C4×#13133182 | 2 |
| #20275691 | 2 |
| #20273213 | 2 |
| #20273143 | 2 |
| #20272547 | 2 |
| C53×#1303 | 2 |
| #9232 | 53 |