Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
542 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21457131 | C2 | semidirect |
| 3. #21446618 | C2 | semidirect |
| 4. #21444434 | C2 | semidirect |
| 5. #21444431 | C2 | semidirect |
| 6. #21443688 | C2 | semidirect |
| 7. C61×#3110 | C2 | semidirect |
| 202. #3110 | D61 | semidirect |
| 239. C61 | #10027 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457131 | 2 |
| #21455910 | 2 |
| #21446618 | 2 |
| #21444434 | 2 |
| #21444431 | 2 |
| #21443688 | 2 |
| C61×#3110 | 2 |
| #10027 | 61 |