Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
328 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21458808 | C2 | semidirect |
| 2. #21448075 | C2 | semidirect |
| 4. #21445179 | C2 | semidirect |
| 5. #21443869 | C2 | semidirect |
| 6. #21443781 | C2 | semidirect |
| 7. C61×Q8⋊C16 | C2 | semidirect |
| 138. Q8⋊C16 | D61 | semidirect |
| 162. C61 | #12331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458808 | 2 |
| #21448075 | 2 |
| #21447855 | 2 |
| #21445179 | 2 |
| #21443869 | 2 |
| #21443781 | 2 |
| C61×Q8⋊C16 | 2 |
| #12331 | 61 |