Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
202 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 83 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. #16810374 | C4 | semidirect |
| 13. C4×C16×C53 | C4 | semidirect |
| 90. C4×C16 | Dic53 | semidirect |
| 95. C53 | #7218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274846 | 2 |
| #20273478 | 2 |
| C53×#2162 | 2 |
| #7218 | 53 |