Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
728 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 179 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. #21456537 | C2 | semidirect |
| 3. #21456213 | C2 | semidirect |
| 4. #21456200 | C2 | semidirect |
| 5. #21445472 | C2 | semidirect |
| 6. #21445465 | C2 | semidirect |
| 7. #21445458 | C2 | semidirect |
| 8. #21445431 | C2 | semidirect |
| 9. C61×#1455 | C2 | semidirect |
| 163. #1455 | D61 | semidirect |
| 197. C61 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456557 | 2 |
| #21456537 | 2 |
| #21456213 | 2 |
| #21456200 | 2 |
| #21445472 | 2 |
| #21445465 | 2 |
| #21445458 | 2 |
| #21445431 | 2 |
| C61×#1455 | 2 |
| #19754 | 61 |