Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 71 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. #21446372 | C2 | semidirect |
| 5. #21446041 | C2 | semidirect |
| 6. #21443941 | C2 | semidirect |
| 7. C61×#2135 | C2 | semidirect |
| 188. #2135 | D61 | semidirect |
| 221. C61 | #13430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456686 | 2 |
| #21447510 | 2 |
| #21446372 | 2 |
| #21446364 | 2 |
| #21446041 | 2 |
| #21443941 | 2 |
| C61×#2135 | 2 |
| #13430 | 61 |