Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
654 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 11. C2×#13133217 | C4 | semidirect |
| 16. #16810522 | C4 | semidirect |
| 19. C53×#384 | C4 | semidirect |
| 26. #13133274 | Q8 | semidirect |
| 205. #384 | #6157 | semidirect |
| 211. C53 | #9884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133274 | 2 |
| #20289893 | 2 |
| #20289588 | 2 |
| #20283068 | 2 |
| #9884 | 53 |