Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
804 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 8. #16811353 | C4 | semidirect |
| 123. Dic106 | #103 | semidirect |
| 168. C53 | #8451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811353 | 2 |
| #20274717 | 2 |
| C2×#16810372 | 2 |
| C2×#16810355 | 2 |
| C53×#1956 | 2 |
| #8451 | 53 |