Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
472 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 472 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. #21454837 | C2 | semidirect |
| 3. #21445630 | C2 | semidirect |
| 4. #21444410 | C2 | semidirect |
| 5. #21444326 | C2 | semidirect |
| 6. #21443690 | C2 | semidirect |
| 7. C61×#1300 | C2 | semidirect |
| 11. #16840048 | C4 | semidirect |
| 12. #16840043 | C4 | semidirect |
| 13. #16839963 | C4 | semidirect |
| 14. #16839958 | C4 | semidirect |
| 202. #1300 | D61 | semidirect |
| 235. C61 | #9162 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455971 | 2 |
| #21454837 | 2 |
| #21445630 | 2 |
| #21444410 | 2 |
| #21444326 | 2 |
| #21443690 | 2 |
| C61×#1300 | 2 |
| #9162 | 61 |