Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
180 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 34. C42×C53 | C16 | semidirect |
| 81. C53 | #7062 | semidirect |
| 108. C42 | #11719908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272655 | 2 |
| C53×#1831 | 2 |
| #7062 | 53 |