Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
478 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #21425069 | C2 | semidirect |
| 4. #21422776 | C2 | semidirect |
| 6. #21421955 | C2 | semidirect |
| 7. C59×#1275 | C2 | semidirect |
| 11. #16837800 | C4 | semidirect |
| 12. #16837749 | C4 | semidirect |
| 174. #1275 | D59 | semidirect |
| 200. C59 | #9287 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21435226 | 2 |
| #21432815 | 2 |
| #21425069 | 2 |
| #21422776 | 2 |
| #21422657 | 2 |
| #21421955 | 2 |
| C59×#1275 | 2 |
| #9287 | 59 |