Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 16. C59×#500 | C4 | semidirect |
| 17. C59×#494 | C4 | semidirect |
| 18. C59×#487 | C4 | semidirect |
| 138. #500 | Dic59 | semidirect |
| 139. #494 | Dic59 | semidirect |
| 140. #487 | Dic59 | semidirect |
| 155. C59 | #9763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21423782 | 2 |
| #21422859 | 2 |
| #21422711 | 2 |
| #21422608 | 2 |
| C59×#3170 | 2 |
| #9763 | 59 |