Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21454806 | C2 | semidirect |
| 3. #21444365 | C2 | semidirect |
| 4. #21444235 | C2 | semidirect |
| 5. #21443683 | C2 | semidirect |
| 6. #21443681 | C2 | semidirect |
| 7. C61×#1521 | C2 | semidirect |
| 9. #16840157 | C4 | semidirect |
| 10. #16840152 | C4 | semidirect |
| 11. #16840132 | C4 | semidirect |
| 12. #16840128 | C4 | semidirect |
| 201. #1521 | D61 | semidirect |
| 239. C61 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456852 | 2 |
| #21454806 | 2 |
| #21444365 | 2 |
| #21444235 | 2 |
| #21443683 | 2 |
| #21443681 | 2 |
| C61×#1521 | 2 |
| #9370 | 61 |