Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
542 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 542 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 |
|---|---|---|
| 1. #21426989 | C2 | semidirect |
| 3. #21424195 | C2 | semidirect |
| 5. #21422001 | C2 | semidirect |
| 6. #21421981 | C2 | semidirect |
| 26. C59×#428 | C4 | semidirect |
| 27. C59×#418 | C4 | semidirect |
| 215. #428 | Dic59 | semidirect |
| 216. #418 | Dic59 | semidirect |
| 231. C59 | #9366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21426989 | 2 |
| #21424933 | 2 |
| #21424195 | 2 |
| #21422612 | 2 |
| #21422001 | 2 |
| #21421981 | 2 |
| C59×#3094 | 2 |
| #9366 | 59 |