Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
318 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 15. C53×#366 | C4 | semidirect |
| 55. C16×C53 | C4⋊C4 | semidirect |
| 108. #366 | Dic53 | semidirect |
| 111. C53 | #13168 | semidirect |
| 152. C16 | C4⋊Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810451 | 2 |
| C2×#16810398 | 2 |
| #20275449 | 2 |
| #20272806 | 2 |
| C2×C53×#366 | 2 |
| #13168 | 53 |