Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
516 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 121 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. #21425074 | C2 | semidirect |
| 4. C4×C8×Dic59 | C2 | semidirect |
| 5. #21422851 | C2 | semidirect |
| 7. C59×#1493 | C2 | semidirect |
| 9. #16837798 | C4 | semidirect |
| 10. #16837776 | C4 | semidirect |
| 11. #16837752 | C4 | semidirect |
| 12. #16837750 | C4 | semidirect |
| 104. C4×Dic59 | SD16 | semidirect |
| 141. C59⋊C8 | #104 | semidirect |
| 166. #1493 | D59 | semidirect |
| 192. C59 | #9843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434656 | 2 |
| #21425074 | 2 |
| #21424923 | 2 |
| C4×C8×Dic59 | 2 |
| #21422851 | 2 |
| #21422548 | 2 |
| C59×#1493 | 2 |
| #9843 | 59 |