Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
462 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 99 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×#16839574 | C2 | semidirect |
| 3. C2×#16839568 | C2 | semidirect |
| 4. #21447529 | C2 | semidirect |
| 5. C2×#16839562 | C2 | semidirect |
| 6. #21443908 | C2 | semidirect |
| 7. C61×#1952 | C2 | semidirect |
| 63. #108×C61 | D4 | semidirect |
| 188. #1952 | D61 | semidirect |
| 216. C61 | #13411 | semidirect |
| 253. #108 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456305 | 2 |
| C2×#16839574 | 2 |
| C2×#16839568 | 2 |
| #21447529 | 2 |
| C2×#16839562 | 2 |
| #21443908 | 2 |
| C61×#1952 | 2 |
| #13411 | 61 |