Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21446664 | C2 | semidirect |
| 5. #21443732 | C2 | semidirect |
| 6. #21443710 | C2 | semidirect |
| 7. C61×#1549 | C2 | semidirect |
| 144. D244 | #101 | semidirect |
| 182. #1549 | D61 | semidirect |
| 214. C61 | #9357 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455628 | 2 |
| #21454940 | 2 |
| #21446664 | 2 |
| #21444256 | 2 |
| #21443732 | 2 |
| #21443710 | 2 |
| C61×#1549 | 2 |
| #9357 | 61 |