Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
488 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 13. C22×C4⋊C4×C59 | C4 | semidirect |
| 20. C59×#385 | C4 | semidirect |
| 21. C59×#385 | C4 | semidirect |
| 22. C59×#380 | C4 | semidirect |
| 196. C22×C4⋊C4 | Dic59 | semidirect |
| 206. #385 | Dic59 | semidirect |
| 207. #385 | Dic59 | semidirect |
| 208. #380 | Dic59 | semidirect |
| 212. C59 | #13297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424088 | 2 |
| C4×#14273642 | 2 |
| #21422214 | 2 |
| C59×#2579 | 2 |
| #13297 | 59 |