Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
798 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 192 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. #16810489 | C4 | semidirect |
| 13. #16810488 | C4 | semidirect |
| 16. C53×#382 | C4 | semidirect |
| 167. #382 | #6157 | semidirect |
| 172. C53 | #11358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811496 | 2 |
| #20290376 | 2 |
| #20289893 | 2 |
| #382×D53 | 2 |
| #11358 | 53 |