Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 131 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×#16810445 | C2 | semidirect |
| 4. #20272813 | C2 | semidirect |
| 11. C22⋊#11719908 | C4 | semidirect |
| 133. C53 | #12930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810445 | 2 |
| #20276326 | 2 |
| #20274753 | 2 |
| #20272813 | 2 |
| C2×C53×#427 | 2 |
| #12930 | 53 |