Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
434 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 434 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. #21422813 | C2 | semidirect |
| 5. #21421966 | C2 | semidirect |
| 6. #21421952 | C2 | semidirect |
| 7. C59×#1981 | C2 | semidirect |
| 9. #16837808 | C4 | semidirect |
| 10. #16837764 | C4 | semidirect |
| 191. #1981 | D59 | semidirect |
| 227. C59 | #9377 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435326 | 2 |
| #21433232 | 2 |
| #21422813 | 2 |
| #21422619 | 2 |
| #21421966 | 2 |
| #21421952 | 2 |
| C59×#1981 | 2 |
| #9377 | 59 |