Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
480 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21425679 | C2 | semidirect |
| 2. #21425548 | C2 | semidirect |
| 4. #21424801 | C2 | semidirect |
| 6. #21424337 | C2 | semidirect |
| 7. #21424314 | C2 | semidirect |
| 8. #21424233 | C2 | semidirect |
| 9. C59×#2102 | C2 | semidirect |
| 137. #2102 | D59 | semidirect |
| 170. C59 | #32702 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425679 | 2 |
| #21425548 | 2 |
| #21425383 | 2 |
| #21424801 | 2 |
| #21424457 | 2 |
| #21424337 | 2 |
| #21424314 | 2 |
| #21424233 | 2 |
| C59×#2102 | 2 |
| #32702 | 59 |