Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
386 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 73 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. #21445993 | C2 | semidirect |
| 3. #21444539 | C2 | semidirect |
| 4. #21444431 | C2 | semidirect |
| 5. #21444430 | C2 | semidirect |
| 6. #21443729 | C2 | semidirect |
| 7. C61×#1557 | C2 | semidirect |
| 160. #1557 | D61 | semidirect |
| 189. C61 | #10524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457197 | 2 |
| #21445993 | 2 |
| #21444539 | 2 |
| #21444431 | 2 |
| #21444430 | 2 |
| #21443729 | 2 |
| C61×#1557 | 2 |
| #10524 | 61 |