Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
392 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 77 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. #21444605 | C2 | semidirect |
| 4. #21444520 | C2 | semidirect |
| 5. #21444317 | C2 | semidirect |
| 7. C61×#1285 | C2 | semidirect |
| 184. #1285 | D61 | semidirect |
| 212. C61 | #10510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456824 | 2 |
| #21446751 | 2 |
| #21444605 | 2 |
| #21444520 | 2 |
| #21444317 | 2 |
| #21444172 | 2 |
| C61×#1285 | 2 |
| #10510 | 61 |