Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 143 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. #20274491 | C2 | semidirect |
| 3. #20272602 | C2 | semidirect |
| 4. #20272600 | C2 | semidirect |
| 10. #16810360 | C4 | semidirect |
| 11. #16810357 | C4 | semidirect |
| 12. C2×#131×C53 | C4 | semidirect |
| 17. C53×#424 | C4 | semidirect |
| 18. C53×#408 | C4 | semidirect |
| 20. C53×#405 | C4 | semidirect |
| 149. C2×#131 | Dic53 | semidirect |
| 154. #424 | Dic53 | semidirect |
| 155. #408 | Dic53 | semidirect |
| 158. #405 | Dic53 | semidirect |
| 164. C53 | #8239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274491 | 2 |
| #20273206 | 2 |
| #20272602 | 2 |
| #20272600 | 2 |
| C53×#2929 | 2 |
| #8239 | 53 |