Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #21444370 | C2 | semidirect |
| 5. #21443684 | C2 | semidirect |
| 6. #21443681 | C2 | semidirect |
| 7. C61×#1485 | C2 | semidirect |
| 9. #16840168 | C4 | semidirect |
| 10. #16840168 | C4 | semidirect |
| 11. #16840124 | C4 | semidirect |
| 12. #16840124 | C4 | semidirect |
| 189. #1485 | D61 | semidirect |
| 224. C61 | #9369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457059 | 2 |
| #21454804 | 2 |
| #21444397 | 2 |
| #21444370 | 2 |
| #21443684 | 2 |
| #21443681 | 2 |
| C61×#1485 | 2 |
| #9369 | 61 |