Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
418 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21422822 | C2 | semidirect |
| 5. #21421966 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#1988 | C2 | semidirect |
| 9. #16837808 | C4 | semidirect |
| 10. #16837764 | C4 | semidirect |
| 185. #1988 | D59 | semidirect |
| 221. C59 | #9375 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435317 | 2 |
| #21433232 | 2 |
| #21422822 | 2 |
| #21422619 | 2 |
| #21421966 | 2 |
| #21421952 | 2 |
| C59×#1988 | 2 |
| #9375 | 59 |