Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1566 conjugacy classes of subgroups; only the 424 normal subgroups are shown.
This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 424 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 |
|---|---|---|
| 9. #16811568 | C4 | semidirect |
| 12. C42×#6157 | C4 | semidirect |
| 14. #16810491 | C4 | semidirect |
| 15. #16810490 | C4 | semidirect |
| 17. C53×#383 | C4 | semidirect |
| 60. C42×C53 | C42 | semidirect |
| 61. C4×Dic53 | C42 | semidirect |
| 97. #6157 | #383 | direct (N × H) |
| 119. #383 | #6157 | direct (N × H) |
| 124. C53 | C4×#383 | semidirect |
| 168. C42 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811568 | 2 |
| C2×C42×#6157 | 2 |
| #20289890 | 2 |
| #95×#6157 | 2 |
| #383×D53 | 2 |
| C4×#383 | 53 |