Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 87 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. #16810650 | C4 | semidirect |
| 13. #16810650 | C4 | semidirect |
| 18. C4×#11719917 | C4 | semidirect |
| 19. C2×C4×#88322 | C4 | semidirect |
| 193. C53 | #12864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283359 | 2 |
| #20274819 | 2 |
| #20272845 | 2 |
| #20272843 | 2 |
| #20272837 | 2 |
| #20272835 | 2 |
| C53×#1827 | 2 |
| #12864 | 53 |