Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
574 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 574 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 |
|---|---|---|
| 1. #21456942 | C2 | semidirect |
| 2. #21456937 | C2 | semidirect |
| 4. #21446638 | C2 | semidirect |
| 5. #21444378 | C2 | semidirect |
| 6. #21443663 | C2 | semidirect |
| 7. C61×#1517 | C2 | semidirect |
| 196. #1517 | D61 | semidirect |
| 228. C61 | #10225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456942 | 2 |
| #21456937 | 2 |
| #21456264 | 2 |
| #21446638 | 2 |
| #21444378 | 2 |
| #21443663 | 2 |
| C61×#1517 | 2 |
| #10225 | 61 |