Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
298 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 61 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. #21447861 | C2 | semidirect |
| 3. #21445305 | C2 | semidirect |
| 4. #21443871 | C2 | semidirect |
| 5. #21443787 | C2 | semidirect |
| 6. #21443778 | C2 | semidirect |
| 7. C61×#2245 | C2 | semidirect |
| 142. #2245 | D61 | semidirect |
| 172. C61 | #12350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458423 | 2 |
| #21447861 | 2 |
| #21445305 | 2 |
| #21443871 | 2 |
| #21443787 | 2 |
| #21443778 | 2 |
| C61×#2245 | 2 |
| #12350 | 61 |