Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
304 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21447592 | C2 | semidirect |
| 5. #21446609 | C2 | semidirect |
| 6. #21443915 | C2 | semidirect |
| 7. C61×#2151 | C2 | semidirect |
| 133. #2151 | D61 | semidirect |
| 159. C61 | #13468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447592 | 2 |
| #21447548 | 2 |
| C2×#16839570 | 2 |
| #21446717 | 2 |
| #21446609 | 2 |
| #21443915 | 2 |
| C61×#2151 | 2 |
| #13468 | 61 |