Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
680 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20277889 | C2 | semidirect |
| 2. C2×#16810420 | C2 | semidirect |
| 3. #20274674 | C2 | semidirect |
| 4. #20272841 | C2 | semidirect |
| 19. C53×#454 | C4 | semidirect |
| 41. 2−1+4×C53 | C2×C4 | semidirect |
| 60. #101×C53 | C2×C4 | semidirect |
| 202. #454 | Dic53 | semidirect |
| 214. C53 | #13055 | semidirect |
| 218. 2−1+4 | C2×Dic53 | semidirect |
| 250. #101 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277889 | 2 |
| C2×#16810420 | 2 |
| #20274674 | 2 |
| #20272841 | 2 |
| C2×C53×#454 | 2 |
| #13055 | 53 |