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. #21422653 | C2 | semidirect |
| 4. #21422626 | C2 | semidirect |
| 5. #21422455 | C2 | semidirect |
| 6. #21422005 | C2 | semidirect |
| 7. C59×#1293 | C2 | semidirect |
| 10. #16837733 | C4 | semidirect |
| 12. #16837716 | C4 | semidirect |
| 15. #16837555 | C4 | semidirect |
| 17. #16837538 | C4 | semidirect |
| 224. #1293 | 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 |
|---|---|
| #21434912 | 2 |
| #21433156 | 2 |
| #21422653 | 2 |
| #21422626 | 2 |
| #21422455 | 2 |
| #21422005 | 2 |
| C59×#1293 | 2 |
| #9332 | 59 |