Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
474 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 1. C2×#16810730 | C2 | semidirect |
| 2. C2×#16810439 | C2 | semidirect |
| 5. #20272814 | C2 | semidirect |
| 6. #20272794 | C2 | semidirect |
| 24. C2×Q32×C53 | C4 | semidirect |
| 25. C2×SD32×C53 | C4 | semidirect |
| 182. C2×Q32 | Dic53 | semidirect |
| 183. C2×SD32 | Dic53 | semidirect |
| 196. C53 | #13038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810730 | 2 |
| C2×#16810439 | 2 |
| C2×#16810433 | 2 |
| #20275609 | 2 |
| #20272814 | 2 |
| #20272794 | 2 |
| C2×C53×#510 | 2 |
| #13038 | 53 |