Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 111 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. #16810915 | C4 | semidirect |
| 11. #16810830 | C4 | semidirect |
| 112. C4×Dic53 | Q16 | semidirect |
| 207. C53 | #9236 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284750 | 2 |
| #20277189 | 2 |
| #20275693 | 2 |
| #20273145 | 2 |
| #20272618 | 2 |
| #20272547 | 2 |
| C53×#1503 | 2 |
| #9236 | 53 |