Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
5990 conjugacy classes of subgroups; only the 699 normal subgroups are shown.
This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 699 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 |
|---|---|---|
| 1. C2×#16810587 | C2 | semidirect |
| 2. #20274625 | C2 | semidirect |
| 4. C22×#11719917 | C22 | semidirect |
| 6. C2×C22⋊#88322 | C22 | semidirect |
| 14. C22×#88322 | C23 | semidirect |
| 39. C24×C53 | M16 | semidirect |
| 92. C22×C53 | #407 | semidirect |
| 114. C53 | #20579 | semidirect |
| 140. C24 | #11719917 | semidirect |
| 193. C22 | #16810587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810587 | 2 |
| #20274625 | 2 |
| C25×C4×C53 | 2 |
| #20579 | 53 |