Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
326 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 9. #16811545 | C4 | semidirect |
| 10. #16811512 | C4 | semidirect |
| 111. C53 | #12665 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811545 | 2 |
| #20290924 | 2 |
| C2×#16811512 | 2 |
| #20289769 | 2 |
| #20274596 | 2 |
| #12665 | 53 |