Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1566 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 280 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 |
|---|---|---|
| 2. #20290612 | C2 | direct (N × H) |
| 13. C2×#13133174 | C4 | semidirect |
| 15. C22×#11719919 | C4 | semidirect |
| 17. C22×C4×Dic53 | C4 | semidirect |
| 18. C22×C42×C53 | C4 | semidirect |
| 36. C2×#11719919 | C2×C4 | semidirect |
| 43. C2×C4×Dic53 | C2×C4 | semidirect |
| 48. C2×C42×C53 | C2×C4 | semidirect |
| 153. C2×C53 | #1820 | semidirect |
| 167. C22×C42 | #6157 | semidirect |
| 172. C53 | C2×#1820 | semidirect |
| 201. C2×C42 | C2×#6157 | semidirect |
| 304. C2 | #20290612 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811566 | 2 |
| #20290612 | 2 |
| C2×#16811501 | 2 |
| C22×#13133174 | 2 |
| C2×#1820 | 53 |