Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
510 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. #21462627 | C2 | semidirect |
| 2. #21461692 | C2 | semidirect |
| 3. #21461200 | C2 | semidirect |
| 4. #21461166 | C2 | semidirect |
| 5. #21460711 | C2 | semidirect |
| 6. #21460653 | C2 | semidirect |
| 27. #16839964 | C4 | semidirect |
| 28. #16839962 | C4 | semidirect |
| 29. #16839958 | C4 | semidirect |
| 32. C61×#462 | C4 | semidirect |
| 242. #462 | #6923 | semidirect |
| 262. C61 | #9210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462627 | 2 |
| #21461692 | 2 |
| #21461200 | 2 |
| #21461166 | 2 |
| #21460711 | 2 |
| #21460653 | 2 |
| #21455277 | 2 |
| #9210 | 61 |