Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
628 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21457011 | C2 | semidirect |
| 3. #21451764 | C2 | semidirect |
| 4. #21444422 | C2 | semidirect |
| 5. #21444328 | C2 | semidirect |
| 6. #21443711 | C2 | semidirect |
| 7. C61×#1555 | C2 | semidirect |
| 187. #1555 | D61 | semidirect |
| 220. C61 | #10089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457011 | 2 |
| #21456269 | 2 |
| #21451764 | 2 |
| #21444422 | 2 |
| #21444328 | 2 |
| #21443711 | 2 |
| C61×#1555 | 2 |
| #10089 | 61 |