Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
382 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 92. C42×C53 | Q16 | semidirect |
| 201. C53 | #10523 | semidirect |
| 281. C42 | #11719925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20286057 | 2 |
| #20275692 | 2 |
| #20274832 | 2 |
| #20273406 | 2 |
| #20273405 | 2 |
| #20272589 | 2 |
| C53×#1994 | 2 |
| #10523 | 53 |