Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. #21423847 | C2 | semidirect |
| 2. #21422859 | C2 | semidirect |
| 3. #21422707 | C2 | semidirect |
| 4. #21422604 | C2 | semidirect |
| 16. C59×#500 | C4 | semidirect |
| 17. C59×#493 | C4 | semidirect |
| 18. C59×#486 | C4 | semidirect |
| 144. #500 | Dic59 | semidirect |
| 145. #493 | Dic59 | semidirect |
| 146. #486 | Dic59 | semidirect |
| 161. C59 | #9764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21423847 | 2 |
| #21422859 | 2 |
| #21422707 | 2 |
| #21422604 | 2 |
| C59×#3169 | 2 |
| #9764 | 59 |