Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
440 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21423784 | C2 | semidirect |
| 3. #21422857 | C2 | semidirect |
| 5. #21422608 | C2 | semidirect |
| 7. C59×#1531 | C2 | semidirect |
| 9. #16837798 | C4 | semidirect |
| 10. #16837776 | C4 | semidirect |
| 11. #16837752 | C4 | semidirect |
| 12. #16837750 | C4 | semidirect |
| 177. #1531 | D59 | semidirect |
| 209. C59 | #9761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434656 | 2 |
| #21423784 | 2 |
| #21422857 | 2 |
| #21422706 | 2 |
| #21422608 | 2 |
| #21422605 | 2 |
| C59×#1531 | 2 |
| #9761 | 59 |