Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
386 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 81 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. #21445956 | C2 | semidirect |
| 3. #21444552 | C2 | semidirect |
| 4. #21444270 | C2 | semidirect |
| 5. #21444269 | C2 | semidirect |
| 6. #21443732 | C2 | semidirect |
| 7. C61×#1560 | C2 | semidirect |
| 171. #1560 | D61 | semidirect |
| 200. C61 | #10531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457197 | 2 |
| #21445956 | 2 |
| #21444552 | 2 |
| #21444270 | 2 |
| #21444269 | 2 |
| #21443732 | 2 |
| C61×#1560 | 2 |
| #10531 | 61 |