Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
366 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 10. #16810448 | C4 | semidirect |
| 11. C16×Dic53 | C4 | semidirect |
| 51. #11719908 | C42 | semidirect |
| 84. Dic53 | #366 | semidirect |
| 104. C53 | C4×#366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810448 | 2 |
| C2×C16×Dic53 | 2 |
| #107×Dic53 | 2 |
| #20272807 | 2 |
| C53×#1380 | 2 |
| C4×#366 | 53 |