Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
688 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 215 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. #21424592 | C2 | semidirect |
| 2. #21424571 | C2 | semidirect |
| 3. #21424490 | C2 | semidirect |
| 5. #21424245 | C2 | semidirect |
| 20. C59×#497 | C4 | semidirect |
| 21. C59×#494 | C4 | semidirect |
| 22. C59×#492 | C4 | semidirect |
| 139. #497 | Dic59 | semidirect |
| 140. #494 | Dic59 | semidirect |
| 141. #492 | Dic59 | semidirect |
| 151. C59 | #23360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21424592 | 2 |
| #21424571 | 2 |
| #21424490 | 2 |
| #21424480 | 2 |
| #21424245 | 2 |
| C59×#3152 | 2 |
| #23360 | 59 |