Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
494 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21444383 | C2 | semidirect |
| 5. #21443722 | C2 | semidirect |
| 6. #21443678 | C2 | semidirect |
| 7. C61×#1503 | C2 | semidirect |
| 10. #16840049 | C4 | semidirect |
| 11. #16840039 | C4 | semidirect |
| 188. #1503 | D61 | semidirect |
| 219. C61 | #9177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455612 | 2 |
| #21448790 | 2 |
| #21444383 | 2 |
| #21444209 | 2 |
| #21443722 | 2 |
| #21443678 | 2 |
| C61×#1503 | 2 |
| #9177 | 61 |