Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
470 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #21454904 | C2 | semidirect |
| 5. #21443716 | C2 | semidirect |
| 6. #21443677 | C2 | semidirect |
| 7. C61×#1805 | C2 | semidirect |
| 11. #16839972 | C4 | semidirect |
| 12. #16839962 | C4 | semidirect |
| 180. #1805 | D61 | semidirect |
| 210. C61 | #9310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455291 | 2 |
| #21454904 | 2 |
| #21444378 | 2 |
| #21444217 | 2 |
| #21443716 | 2 |
| #21443677 | 2 |
| C61×#1805 | 2 |
| #9310 | 61 |