Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
438 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 438 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. #21454808 | C2 | semidirect |
| 3. #21444437 | C2 | semidirect |
| 4. C2×#16839501 | C2 | semidirect |
| 5. #21444170 | C2 | semidirect |
| 6. #21443719 | C2 | semidirect |
| 7. C61×#1281 | C2 | semidirect |
| 212. #1281 | D61 | semidirect |
| 247. C61 | #9265 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456786 | 2 |
| #21454808 | 2 |
| #21444437 | 2 |
| C2×#16839501 | 2 |
| #21444170 | 2 |
| #21443719 | 2 |
| C61×#1281 | 2 |
| #9265 | 61 |