Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21454427 | C2 | semidirect |
| 3. C2×#16839576 | C2 | semidirect |
| 4. C2×#16839574 | C2 | semidirect |
| 5. #21447448 | C2 | semidirect |
| 6. #21443930 | C2 | semidirect |
| 7. C61×#1385 | C2 | semidirect |
| 169. #1385 | D61 | semidirect |
| 194. C61 | #13007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840033 | 2 |
| #21454427 | 2 |
| C2×#16839576 | 2 |
| C2×#16839574 | 2 |
| #21447448 | 2 |
| #21443930 | 2 |
| C61×#1385 | 2 |
| #13007 | 61 |