Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
716 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #20285487 | C2 | semidirect |
| 4. #20273080 | C2 | semidirect |
| 5. #20273079 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 270. C53 | #9976 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285487 | 2 |
| #20283975 | 2 |
| #20274627 | 2 |
| #20273080 | 2 |
| #20273079 | 2 |
| #20272591 | 2 |
| C53×#3007 | 2 |
| #9976 | 53 |