Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 91 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×#16839584 | C2 | semidirect |
| 3. C2×#16839579 | C2 | semidirect |
| 4. C2×#16839577 | C2 | semidirect |
| 7. C61×#1383 | C2 | semidirect |
| 164. #1383 | D61 | semidirect |
| 187. C61 | #13399 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840021 | 2 |
| C2×#16839584 | 2 |
| C2×#16839579 | 2 |
| C2×#16839577 | 2 |
| C2×#16839543 | 2 |
| #21445858 | 2 |
| C61×#1383 | 2 |
| #13399 | 61 |