Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
542 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 119 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. #21427282 | C2 | semidirect |
| 3. C2×#16837144 | C2 | semidirect |
| 4. #21421978 | C2 | semidirect |
| 17. C59×#490 | C4 | semidirect |
| 144. #490 | Dic59 | semidirect |
| 155. C59 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427282 | 2 |
| #21424921 | 2 |
| C2×#16837144 | 2 |
| #21421978 | 2 |
| C2×C59×#490 | 2 |
| #9002 | 59 |