Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
354 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 354 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. #21425882 | C2 | semidirect |
| 2. C2×#16837222 | C2 | semidirect |
| 6. #21424842 | C2 | semidirect |
| 7. C59×#1387 | C2 | semidirect |
| 147. #1387 | D59 | semidirect |
| 171. C59 | #13478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425882 | 2 |
| C2×#16837222 | 2 |
| C2×#16837214 | 2 |
| #21425813 | 2 |
| #21424960 | 2 |
| #21424842 | 2 |
| C59×#1387 | 2 |
| #13478 | 59 |