Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21454989 | C2 | semidirect |
| 3. #21446651 | C2 | semidirect |
| 4. #21444289 | C2 | semidirect |
| 5. #21443712 | C2 | semidirect |
| 6. #21443710 | C2 | semidirect |
| 7. C61×#1500 | C2 | semidirect |
| 9. #16840172 | C4 | semidirect |
| 10. #16840152 | C4 | semidirect |
| 11. #16840128 | C4 | semidirect |
| 12. #16840121 | C4 | semidirect |
| 213. #1500 | D61 | semidirect |
| 250. C61 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456415 | 2 |
| #21454989 | 2 |
| #21446651 | 2 |
| #21444289 | 2 |
| #21443712 | 2 |
| #21443710 | 2 |
| C61×#1500 | 2 |
| #8997 | 61 |