Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
642 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 194 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. #20290815 | C2 | semidirect |
| 3. #20290773 | C2 | semidirect |
| 5. #20290647 | C2 | semidirect |
| 6. #20290642 | C2 | semidirect |
| 66. C42×C53 | M16 | semidirect |
| 143. C53 | #23378 | semidirect |
| 194. C42 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290815 | 2 |
| #20290790 | 2 |
| #20290773 | 2 |
| #20290661 | 2 |
| #20290647 | 2 |
| #20290642 | 2 |
| #20277263 | 2 |
| #23378 | 53 |