Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 314 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 |
|---|---|---|
| 3. #21445982 | C2 | semidirect |
| 4. #21443928 | C2 | semidirect |
| 5. #21443927 | C2 | semidirect |
| 6. #21443900 | C2 | semidirect |
| 168. C61 | #13485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447531 | 2 |
| #21446708 | 2 |
| #21445982 | 2 |
| #21443928 | 2 |
| #21443927 | 2 |
| #21443900 | 2 |
| C61×#2139 | 2 |
| #13485 | 61 |