Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
728 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21425074 | C2 | semidirect |
| 3. #21425072 | C2 | semidirect |
| 5. #21422833 | C2 | semidirect |
| 7. C59×#1561 | C2 | semidirect |
| 8. #16838156 | C4 | semidirect |
| 226. #1561 | D59 | semidirect |
| 259. C59 | #8531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21438507 | 2 |
| #21425074 | 2 |
| #21425072 | 2 |
| #21424923 | 2 |
| #21422833 | 2 |
| #21422829 | 2 |
| C59×#1561 | 2 |
| #8531 | 59 |