Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 464 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 |
|---|---|---|
| 1. #20276326 | C2 | semidirect |
| 2. #20274740 | C2 | semidirect |
| 3. #20272724 | C2 | semidirect |
| 9. C22⋊#11719908 | C22 | semidirect |
| 10. #16810386 | C22 | semidirect |
| 11. C22×D8×C53 | C4 | semidirect |
| 16. C53×#466 | C4 | semidirect |
| 18. C2×#107×C53 | C4 | semidirect |
| 159. C22×D8 | Dic53 | semidirect |
| 165. #466 | Dic53 | semidirect |
| 167. C2×#107 | Dic53 | semidirect |
| 174. C53 | #11888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276326 | 2 |
| #20274740 | 2 |
| #20272724 | 2 |
| C2×C53×#466 | 2 |
| #11888 | 53 |