Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
476 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 123 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. #21425678 | C2 | semidirect |
| 2. #21425671 | C2 | semidirect |
| 3. #21425552 | C2 | semidirect |
| 5. #21424807 | C2 | semidirect |
| 7. #21424335 | C2 | semidirect |
| 8. #21424317 | C2 | semidirect |
| 9. C59×#1838 | C2 | semidirect |
| 139. #1838 | D59 | semidirect |
| 165. C59 | #32703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425678 | 2 |
| #21425671 | 2 |
| #21425552 | 2 |
| #21425383 | 2 |
| #21424807 | 2 |
| #21424459 | 2 |
| #21424335 | 2 |
| #21424317 | 2 |
| C59×#1838 | 2 |
| #32703 | 59 |