Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 454 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. #16811003 | C4 | semidirect |
| 11. #16810974 | C4 | semidirect |
| 104. C4×Dic53 | Q16 | semidirect |
| 192. C53 | #9297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285665 | 2 |
| #20277461 | 2 |
| #20275695 | 2 |
| #20273397 | 2 |
| #20273278 | 2 |
| #20272543 | 2 |
| C53×#1286 | 2 |
| #9297 | 53 |