Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
458 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 458 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. C2×#16839576 | C2 | semidirect |
| 3. C2×#16839574 | C2 | semidirect |
| 4. C2×#16839543 | C2 | semidirect |
| 5. #21445858 | C2 | semidirect |
| 6. #21443917 | C2 | semidirect |
| 7. C2×C61×#365 | C2 | semidirect |
| 56. M32×C61 | D4 | semidirect |
| 167. C2×#365 | D61 | semidirect |
| 196. C61 | #13398 | semidirect |
| 223. M32 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840016 | 2 |
| C2×#16839576 | 2 |
| C2×#16839574 | 2 |
| C2×#16839543 | 2 |
| #21445858 | 2 |
| #21443917 | 2 |
| C2×C61×#365 | 2 |
| #13398 | 61 |