Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2078 conjugacy classes of subgroups; only the 752 normal subgroups are shown.
This group has 2078 conjugacy classes of subgroups — too many to draw. Only its 752 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 |
|---|---|---|
| 6. C4×C4⋊#6157 | C4 | semidirect |
| 9. #16810469 | C4 | semidirect |
| 10. #16810468 | C4 | semidirect |
| 12. C53×#376 | C4 | semidirect |
| 39. C4⋊#6157 | C42 | semidirect |
| 41. C42×C53 | C42 | semidirect |
| 42. C4×Dic53 | C42 | semidirect |
| 43. C4×Dic53 | C42 | semidirect |
| 86. #376 | #6157 | semidirect |
| 89. C53 | #13750 | semidirect |
| 120. C42 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊#6157 | 2 |
| #95×#6157 | 2 |
| #376×D53 | 2 |
| #13750 | 53 |