Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
366 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 10. #16837229 | C4 | semidirect |
| 11. C16×Dic59 | C4 | semidirect |
| 51. C59⋊C16 | C42 | semidirect |
| 84. Dic59 | #367 | semidirect |
| 104. C59 | C4×#367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837229 | 2 |
| C2×C16×Dic59 | 2 |
| #107×Dic59 | 2 |
| #21422188 | 2 |
| C59×#1380 | 2 |
| C4×#367 | 59 |