Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1774 conjugacy classes of subgroups; only the 432 normal subgroups are shown.
This group has 1774 conjugacy classes of subgroups — too many to draw. Only its 432 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. #16810469 | C4 | semidirect |
| 10. #16810468 | C4 | semidirect |
| 12. C53×#376 | C4 | semidirect |
| 42. C42×C53 | C4⋊C4 | semidirect |
| 43. C4×Dic53 | C4⋊C4 | semidirect |
| 44. C4×Dic53 | C4⋊C4 | semidirect |
| 87. #376 | #6157 | semidirect |
| 90. C53 | #13856 | semidirect |
| 122. 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 |
| #20289903 | 2 |
| #376×D53 | 2 |
| #13856 | 53 |