Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
378 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21425892 | C2 | semidirect |
| 3. #21424222 | C2 | semidirect |
| 4. #21422106 | C2 | semidirect |
| 5. #21422105 | C2 | semidirect |
| 6. #21422104 | C2 | semidirect |
| 7. C59×#1347 | C2 | semidirect |
| 9. #16837806 | C4 | semidirect |
| 10. #16837777 | C4 | semidirect |
| 14. D8×Dic59 | C4 | semidirect |
| 15. #16837484 | C4 | semidirect |
| 172. #1347 | D59 | semidirect |
| 199. C59 | #11856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21434670 | 2 |
| #21425892 | 2 |
| #21424222 | 2 |
| #21422106 | 2 |
| #21422105 | 2 |
| #21422104 | 2 |
| C59×#1347 | 2 |
| #11856 | 59 |