Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21456567 | C2 | semidirect |
| 2. #21455071 | C2 | semidirect |
| 3. #21445731 | C2 | semidirect |
| 4. #21444180 | C2 | semidirect |
| 5. #21444179 | C2 | semidirect |
| 6. #21443695 | C2 | semidirect |
| 7. C61×#3006 | C2 | semidirect |
| 249. #3006 | D61 | semidirect |
| 288. C61 | #9974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456567 | 2 |
| #21455071 | 2 |
| #21445731 | 2 |
| #21444180 | 2 |
| #21444179 | 2 |
| #21443695 | 2 |
| C61×#3006 | 2 |
| #9974 | 61 |