Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
506 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 113 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. #21424233 | C2 | semidirect |
| 3. #21422768 | C2 | semidirect |
| 6. #21422389 | C2 | semidirect |
| 7. C59×#1546 | C2 | semidirect |
| 153. #1546 | D59 | semidirect |
| 180. C59 | #9777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16837776 | 2 |
| #21424233 | 2 |
| #21422768 | 2 |
| #21422765 | 2 |
| #21422763 | 2 |
| #21422389 | 2 |
| C59×#1546 | 2 |
| #9777 | 59 |