Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21444536 | C2 | semidirect |
| 5. #21444331 | C2 | semidirect |
| 6. #21443713 | C2 | semidirect |
| 7. C61×#3165 | C2 | semidirect |
| 176. #3165 | D61 | semidirect |
| 210. C61 | #10100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456818 | 2 |
| #21451760 | 2 |
| #21444536 | 2 |
| #21444416 | 2 |
| #21444331 | 2 |
| #21443713 | 2 |
| C61×#3165 | 2 |
| #10100 | 61 |