Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21446607 | C2 | semidirect |
| 5. #21443912 | C2 | semidirect |
| 6. #21443909 | C2 | semidirect |
| 7. C61×#2161 | C2 | semidirect |
| 17. #16839579 | C4 | semidirect |
| 18. #16839576 | C4 | semidirect |
| 138. #2161 | D61 | semidirect |
| 166. C61 | #12942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454735 | 2 |
| #21447569 | 2 |
| C2×#16839568 | 2 |
| #21446607 | 2 |
| #21443912 | 2 |
| #21443909 | 2 |
| C61×#2161 | 2 |
| #12942 | 61 |