Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21427404 | C2 | semidirect |
| 5. #21421997 | C2 | semidirect |
| 6. #21421924 | C2 | semidirect |
| 7. C59×#1303 | C2 | semidirect |
| 188. #1303 | D59 | semidirect |
| 215. C59 | #10372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427404 | 2 |
| #21424927 | 2 |
| #21422592 | 2 |
| #21422590 | 2 |
| #21421997 | 2 |
| #21421924 | 2 |
| C59×#1303 | 2 |
| #10372 | 59 |