Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
380 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 96 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⋊#364 | C2 | semidirect |
| 2. #21461023 | C2 | semidirect |
| 3. #21460784 | C2 | semidirect |
| 4. #21460783 | C2 | semidirect |
| 9. #16840684 | C22 | semidirect |
| 10. #16840603 | C22 | semidirect |
| 30. #14519800 | C8 | semidirect |
| 34. #14519796 | C8 | semidirect |
| 35. Q16×D61 | C8 | semidirect |
| 37. D8×D61 | C8 | semidirect |
| 194. C61 | #11604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#364 | 2 |
| #21461023 | 2 |
| #21460784 | 2 |
| #21460783 | 2 |
| #443×D61 | 2 |
| #11604 | 61 |