Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
784 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21424039 | C2 | semidirect |
| 3. C4×#14273642 | C2 | semidirect |
| 4. #21421981 | C2 | semidirect |
| 5. C59×#2973 | C2 | semidirect |
| 10. #16837322 | C4 | semidirect |
| 11. #16837319 | C4 | semidirect |
| 13. #16837314 | C4 | semidirect |
| 14. #16837311 | C4 | semidirect |
| 53. C2×M16×C59 | D4 | semidirect |
| 131. C23×C59 | #104 | semidirect |
| 212. #2973 | D59 | semidirect |
| 244. C59 | #9009 | semidirect |
| 256. C2×M16 | C22⋊D59 | semidirect |
| 358. C23 | #14273653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21427311 | 2 |
| #21424039 | 2 |
| C4×#14273642 | 2 |
| #21421981 | 2 |
| C59×#2973 | 2 |
| #9009 | 59 |