Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
408 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21445973 | C2 | semidirect |
| 3. #21444515 | C2 | semidirect |
| 4. #21444514 | C2 | semidirect |
| 5. #21444326 | C2 | semidirect |
| 6. #21443688 | C2 | semidirect |
| 7. C61×#1505 | C2 | semidirect |
| 165. #1505 | D61 | semidirect |
| 192. C61 | #10512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457126 | 2 |
| #21445973 | 2 |
| #21444515 | 2 |
| #21444514 | 2 |
| #21444326 | 2 |
| #21443688 | 2 |
| C61×#1505 | 2 |
| #10512 | 61 |