Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
540 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 89 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. #21454889 | C2 | semidirect |
| 3. #21444533 | C2 | semidirect |
| 4. #21444453 | C2 | semidirect |
| 5. #21443692 | C2 | semidirect |
| 6. #21443690 | C2 | semidirect |
| 7. C61×#1555 | C2 | semidirect |
| 161. #1555 | D61 | semidirect |
| 188. C61 | #9423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456269 | 2 |
| #21454889 | 2 |
| #21444533 | 2 |
| #21444453 | 2 |
| #21443692 | 2 |
| #21443690 | 2 |
| C61×#1555 | 2 |
| #9423 | 61 |