Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2302 conjugacy classes of subgroups; only the 832 normal subgroups are shown.
This group has 2302 conjugacy classes of subgroups — too many to draw. Only its 832 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 |
|---|---|---|
| 8. #16811559 | C4 | semidirect |
| 10. C42×#6157 | C4 | semidirect |
| 12. #16810469 | C4 | semidirect |
| 13. #16810468 | C4 | semidirect |
| 15. C53×#376 | C4 | semidirect |
| 50. C4×#6157 | C42 | semidirect |
| 51. C42×C53 | C42 | semidirect |
| 52. C4×Dic53 | C42 | semidirect |
| 53. C4×Dic53 | C42 | semidirect |
| 81. #6157 | #376 | direct (N × H) |
| 101. #376 | #6157 | direct (N × H) |
| 105. C53 | C4×#376 | semidirect |
| 143. C42 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811559 | 2 |
| C2×C42×#6157 | 2 |
| #95×#6157 | 2 |
| #376×D53 | 2 |
| C4×#376 | 53 |