Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
538 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 99 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. C59×#380 | C4 | semidirect |
| 10. C4×C22⋊C4×C59 | C4 | semidirect |
| 103. #380 | Dic59 | semidirect |
| 106. C4×C22⋊C4 | Dic59 | semidirect |
| 108. C59 | #8750 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424170 | 2 |
| C59⋊#1304 | 2 |
| C59×#2312 | 2 |
| #8750 | 59 |