Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #16811098 | C4 | semidirect |
| 6. C2×#13133134 | C4 | semidirect |
| 9. #16810416 | C4 | semidirect |
| 14. C53×#331 | C4 | semidirect |
| 148. #331 | Dic53 | semidirect |
| 149. C53 | #7493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810416 | 2 |
| #20275114 | 2 |
| C53×#1555 | 2 |
| #7493 | 53 |