Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1276 conjugacy classes of subgroups; only the 260 normal subgroups are shown.
This group has 1276 conjugacy classes of subgroups — too many to draw. Only its 260 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 |
|---|---|---|
| 2. #20290626 | C2 | semidirect |
| 3. #20290413 | C2 | semidirect |
| 12. #16811100 | C4 | semidirect |
| 13. #16811098 | C4 | semidirect |
| 16. C2×#13133173 | C4 | semidirect |
| 18. C53×#518 | C4 | semidirect |
| 167. #518 | #6157 | semidirect |
| 176. C53 | #20710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811603 | 2 |
| #20290626 | 2 |
| #20290413 | 2 |
| #20287913 | 2 |
| #20710 | 53 |