Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
386 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 75 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. #21445994 | C2 | semidirect |
| 3. #21444542 | C2 | semidirect |
| 4. #21444541 | C2 | semidirect |
| 5. #21444429 | C2 | semidirect |
| 6. #21443729 | C2 | semidirect |
| 7. C61×#1530 | C2 | semidirect |
| 162. #1530 | 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 |
| #21445994 | 2 |
| #21444542 | 2 |
| #21444541 | 2 |
| #21444429 | 2 |
| #21443729 | 2 |
| C61×#1530 | 2 |
| #10524 | 61 |