Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
432 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16839583 | C2 | semidirect |
| 3. C2×#16839574 | C2 | semidirect |
| 4. #21447531 | C2 | semidirect |
| 5. #21446685 | C2 | semidirect |
| 6. #21443929 | C2 | semidirect |
| 7. C61×#1974 | C2 | semidirect |
| 174. #1974 | D61 | semidirect |
| 203. C61 | #13445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840197 | 2 |
| C2×#16839583 | 2 |
| C2×#16839574 | 2 |
| #21447531 | 2 |
| #21446685 | 2 |
| #21443929 | 2 |
| C61×#1974 | 2 |
| #13445 | 61 |