Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
358 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21447593 | C2 | semidirect |
| 3. C2×#16839586 | C2 | semidirect |
| 6. #21443925 | C2 | semidirect |
| 7. C61×#1388 | C2 | semidirect |
| 9. #16840180 | C4 | semidirect |
| 138. #1388 | D61 | semidirect |
| 161. C61 | #12833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458921 | 2 |
| #21447593 | 2 |
| C2×#16839586 | 2 |
| #21445875 | 2 |
| #21445874 | 2 |
| #21443925 | 2 |
| C61×#1388 | 2 |
| #12833 | 61 |