Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
6494 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 6494 conjugacy classes of subgroups — too many to draw. Only its 675 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 |
|---|---|---|
| 2. C2×#16837274 | C2 | semidirect |
| 4. #21422318 | C2 | semidirect |
| 9. C22×Dic59⋊C4 | C22 | semidirect |
| 12. #16837258 | C4 | semidirect |
| 13. C2×C59⋊#95 | C22 | semidirect |
| 29. C2×C22⋊Dic59 | C2×C4 | semidirect |
| 51. C24×C59 | C4⋊C4 | semidirect |
| 72. C22×Dic59 | C22×C4 | semidirect |
| 120. C22×C59 | #385 | semidirect |
| 155. C59 | #14693 | semidirect |
| 189. C24 | Dic59⋊C4 | semidirect |
| 257. C22 | #16837274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic59 | 2 |
| C2×#16837274 | 2 |
| C2×#16837258 | 2 |
| #21422318 | 2 |
| C2×C59×#379 | 2 |
| #14693 | 59 |