Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 91 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. #21445831 | C2 | semidirect |
| 3. #21444591 | C2 | semidirect |
| 6. #21444142 | C2 | semidirect |
| 7. C61×#1286 | C2 | semidirect |
| 182. #1286 | D61 | semidirect |
| 208. C61 | #10467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455293 | 2 |
| #21445831 | 2 |
| #21444591 | 2 |
| #21444466 | 2 |
| #21444378 | 2 |
| #21444142 | 2 |
| C61×#1286 | 2 |
| #10467 | 61 |