Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #21426845 | C2 | semidirect |
| 5. #21421956 | C2 | semidirect |
| 6. #21421924 | C2 | semidirect |
| 7. C59×#1548 | C2 | semidirect |
| 9. #16837776 | C4 | semidirect |
| 10. #16837752 | C4 | semidirect |
| 111. C4×Dic59 | SD16 | semidirect |
| 180. #1548 | D59 | semidirect |
| 209. C59 | #9301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435021 | 2 |
| #21426845 | 2 |
| #21424927 | 2 |
| #21422657 | 2 |
| #21421956 | 2 |
| #21421924 | 2 |
| C59×#1548 | 2 |
| #9301 | 59 |