Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 20. C53×#498 | C4 | semidirect |
| 21. C53×#494 | C4 | semidirect |
| 22. C53×#487 | C4 | semidirect |
| 23. C53×#487 | C4 | semidirect |
| 157. #498 | Dic53 | semidirect |
| 158. #494 | Dic53 | semidirect |
| 159. #487 | Dic53 | semidirect |
| 160. #487 | Dic53 | semidirect |
| 174. C53 | #9416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283821 | 2 |
| #20273353 | 2 |
| #20273266 | 2 |
| #20272587 | 2 |
| #20272580 | 2 |
| C53×#3185 | 2 |
| #9416 | 53 |