Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
794 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 12. #16810492 | C4 | semidirect |
| 13. #16810489 | C4 | semidirect |
| 16. C53×#382 | C4 | semidirect |
| 156. #382 | #6157 | semidirect |
| 162. C53 | #11359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811493 | 2 |
| #20290379 | 2 |
| C4×(C2×#6157)⋊C4 | 2 |
| #20277121 | 2 |
| #11359 | 53 |