Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 452 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. #21454991 | C2 | semidirect |
| 3. #21446652 | C2 | semidirect |
| 4. #21444306 | C2 | semidirect |
| 5. #21443711 | C2 | semidirect |
| 6. #21443710 | C2 | semidirect |
| 7. C61×#1496 | C2 | semidirect |
| 9. #16840168 | C4 | semidirect |
| 10. #16840149 | C4 | semidirect |
| 11. #16840126 | C4 | semidirect |
| 12. #16840124 | C4 | semidirect |
| 214. #1496 | D61 | semidirect |
| 250. C61 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456408 | 2 |
| #21454991 | 2 |
| #21446652 | 2 |
| #21444306 | 2 |
| #21443711 | 2 |
| #21443710 | 2 |
| C61×#1496 | 2 |
| #8997 | 61 |