Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21454833 | C2 | semidirect |
| 3. #21444418 | C2 | semidirect |
| 4. #21444170 | C2 | semidirect |
| 5. #21443729 | C2 | semidirect |
| 6. #21443710 | C2 | semidirect |
| 7. C61×#1488 | C2 | semidirect |
| 205. #1488 | D61 | semidirect |
| 240. C61 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455313 | 2 |
| #21454833 | 2 |
| #21444418 | 2 |
| #21444170 | 2 |
| #21443729 | 2 |
| #21443710 | 2 |
| C61×#1488 | 2 |
| #9349 | 61 |