Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 3. #21421974 | C2 | semidirect |
| 4. #21421963 | C2 | semidirect |
| 10. #16837270 | C4 | semidirect |
| 11. #16837265 | C4 | semidirect |
| 14. C4×C22⋊Dic59 | C4 | semidirect |
| 15. #16837248 | C4 | semidirect |
| 203. C59 | #8763 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427036 | 2 |
| #21422414 | 2 |
| #21421974 | 2 |
| #21421963 | 2 |
| C59×#1799 | 2 |
| #8763 | 59 |