Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#16839885 | C2 | semidirect |
| 3. #21447569 | C2 | semidirect |
| 4. #21447548 | C2 | semidirect |
| 5. #21446712 | C2 | semidirect |
| 6. #21443931 | C2 | semidirect |
| 7. C61×#1377 | C2 | semidirect |
| 12. #16840205 | C4 | semidirect |
| 14. #16840200 | C4 | semidirect |
| 182. #1377 | D61 | semidirect |
| 210. C61 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458955 | 2 |
| C2×#16839885 | 2 |
| #21447569 | 2 |
| #21447548 | 2 |
| #21446712 | 2 |
| #21443931 | 2 |
| C61×#1377 | 2 |
| #13024 | 61 |