Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 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. #21423847 | C2 | semidirect |
| 3. #21422712 | C2 | semidirect |
| 5. #21422609 | C2 | semidirect |
| 7. C59×#1568 | C2 | semidirect |
| 10. #16837800 | C4 | semidirect |
| 11. #16837775 | C4 | semidirect |
| 12. #16837753 | C4 | semidirect |
| 13. #16837749 | C4 | semidirect |
| 174. #1568 | D59 | semidirect |
| 207. C59 | #9766 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434655 | 2 |
| #21423847 | 2 |
| #21422712 | 2 |
| #21422708 | 2 |
| #21422609 | 2 |
| #21422605 | 2 |
| C59×#1568 | 2 |
| #9766 | 59 |