Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
390 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 73 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. #21429748 | C2 | semidirect |
| 5. #21421988 | C2 | semidirect |
| 6. #21421962 | C2 | semidirect |
| 7. C59×#1285 | C2 | semidirect |
| 181. #1285 | D59 | semidirect |
| 207. C59 | #10380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21429748 | 2 |
| #21425014 | 2 |
| #21422644 | 2 |
| #21422605 | 2 |
| #21421988 | 2 |
| #21421962 | 2 |
| C59×#1285 | 2 |
| #10380 | 59 |