Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
546 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. #21421966 | C2 | semidirect |
| 4. #21421965 | C2 | semidirect |
| 5. C59×#1290 | C2 | semidirect |
| 138. #1290 | D59 | semidirect |
| 159. C59 | #7986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #432×D59 | 2 |
| C2×#16837454 | 2 |
| #21421966 | 2 |
| #21421965 | 2 |
| C59×#1290 | 2 |
| #7986 | 59 |