Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
504 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21454873 | C2 | semidirect |
| 3. #21444324 | C2 | semidirect |
| 4. C2×#16839496 | C2 | semidirect |
| 5. #21443706 | C2 | semidirect |
| 6. #21443661 | C2 | semidirect |
| 7. C61×#1471 | C2 | semidirect |
| 9. #16840097 | C4 | semidirect |
| 11. #16840080 | C4 | semidirect |
| 14. #16839913 | C4 | semidirect |
| 16. #16839896 | C4 | semidirect |
| 240. #1471 | D61 | semidirect |
| 280. C61 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456584 | 2 |
| #21454873 | 2 |
| #21444324 | 2 |
| C2×#16839496 | 2 |
| #21443706 | 2 |
| #21443661 | 2 |
| C61×#1471 | 2 |
| #9264 | 61 |