Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #21456722 | C2 | semidirect |
| 2. #21447731 | C2 | semidirect |
| 3. #21446926 | C2 | semidirect |
| 4. #21443837 | C2 | semidirect |
| 5. #21443835 | C2 | semidirect |
| 6. #21443744 | C2 | semidirect |
| 7. C61×#2187 | C2 | semidirect |
| 179. #2187 | D61 | semidirect |
| 211. C61 | #12110 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456722 | 2 |
| #21447731 | 2 |
| #21446926 | 2 |
| #21443837 | 2 |
| #21443835 | 2 |
| #21443744 | 2 |
| C61×#2187 | 2 |
| #12110 | 61 |