Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 3. #21444370 | C2 | semidirect |
| 5. #21443692 | C2 | semidirect |
| 6. #21443685 | C2 | semidirect |
| 7. C61×#2987 | C2 | semidirect |
| 9. #16840165 | C4 | semidirect |
| 10. #16840136 | C4 | semidirect |
| 11. #16840112 | C4 | semidirect |
| 12. #16840110 | C4 | semidirect |
| 152. #2987 | D61 | semidirect |
| 182. C61 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456538 | 2 |
| #21444453 | 2 |
| #21444370 | 2 |
| #21444367 | 2 |
| #21443692 | 2 |
| #21443685 | 2 |
| C61×#2987 | 2 |
| #9418 | 61 |