Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
464 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21433156 | C2 | semidirect |
| 3. #21422650 | C2 | semidirect |
| 4. #21422456 | C2 | semidirect |
| 5. #21422004 | C2 | semidirect |
| 6. #21421972 | C2 | semidirect |
| 7. C59×#1510 | C2 | semidirect |
| 9. #16837732 | C4 | semidirect |
| 11. #16837715 | C4 | semidirect |
| 14. #16837553 | C4 | semidirect |
| 16. #16837536 | C4 | semidirect |
| 221. #1510 | D59 | semidirect |
| 260. C59 | #9332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434910 | 2 |
| #21433156 | 2 |
| #21422650 | 2 |
| #21422456 | 2 |
| #21422004 | 2 |
| #21421972 | 2 |
| C59×#1510 | 2 |
| #9332 | 59 |