Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21424173 | C2 | semidirect |
| 4. #21421950 | C2 | semidirect |
| 5. C59×#2921 | C2 | semidirect |
| 9. #16837303 | C4 | semidirect |
| 10. #16837303 | C4 | semidirect |
| 13. #16837271 | C4 | semidirect |
| 14. #16837267 | C4 | semidirect |
| 182. #2921 | D59 | semidirect |
| 213. C59 | #9446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21428554 | 2 |
| #21424173 | 2 |
| #21422626 | 2 |
| #21421950 | 2 |
| C59×#2921 | 2 |
| #9446 | 59 |