Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21447566 | C2 | semidirect |
| 3. #21447556 | C2 | semidirect |
| 4. #21447448 | C2 | semidirect |
| 5. #21445874 | C2 | semidirect |
| 6. #21443926 | C2 | semidirect |
| 7. C2×C61×#365 | C2 | semidirect |
| 61. M32×C61 | D4 | semidirect |
| 174. C2×#365 | D61 | semidirect |
| 205. C61 | #13400 | semidirect |
| 234. M32 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455482 | 2 |
| #21447566 | 2 |
| #21447556 | 2 |
| #21447448 | 2 |
| #21445874 | 2 |
| #21443926 | 2 |
| C2×C61×#365 | 2 |
| #13400 | 61 |