Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
472 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21423906 | C2 | semidirect |
| 3. #21422687 | C2 | semidirect |
| 4. #21422605 | C2 | semidirect |
| 5. #21421990 | C2 | semidirect |
| 6. #21421969 | C2 | semidirect |
| 7. C59×#2971 | C2 | semidirect |
| 10. #16837687 | C4 | semidirect |
| 11. #16837682 | C4 | semidirect |
| 12. #16837602 | C4 | semidirect |
| 13. #16837597 | C4 | semidirect |
| 198. #2971 | D59 | semidirect |
| 235. C59 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434247 | 2 |
| #21423906 | 2 |
| #21422687 | 2 |
| #21422605 | 2 |
| #21421990 | 2 |
| #21421969 | 2 |
| C59×#2971 | 2 |
| #9162 | 59 |