Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1234 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1234 conjugacy classes of subgroups — too many to draw. Only its 224 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 |
|---|---|---|
| 1. D61⋊#432 | C2 | semidirect |
| 2. #21461300 | C2 | semidirect |
| 3. #21461290 | C2 | semidirect |
| 6. #16840784 | C22 | semidirect |
| 11. #16840721 | C22 | semidirect |
| 12. #16840618 | C22 | semidirect |
| 195. C61 | #17675 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#432 | 2 |
| #21461300 | 2 |
| #21461290 | 2 |
| C2×#16840313 | 2 |
| #17675 | 61 |