Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
378 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 378 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 |
|---|---|---|
| 3. #21447540 | C2 | semidirect |
| 4. #21446734 | C2 | semidirect |
| 6. #21443934 | C2 | semidirect |
| 7. C61×#2153 | C2 | semidirect |
| 159. #2153 | D61 | semidirect |
| 189. C61 | #13443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840205 | 2 |
| #21447569 | 2 |
| #21447540 | 2 |
| #21446734 | 2 |
| #21446717 | 2 |
| #21443934 | 2 |
| C61×#2153 | 2 |
| #13443 | 61 |