Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
464 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21448029 | C2 | semidirect |
| 3. #21448023 | C2 | semidirect |
| 4. #21447980 | C2 | semidirect |
| 5. #21447928 | C2 | semidirect |
| 6. C4×Dic488 | C2 | semidirect |
| 8. #21447606 | C2 | semidirect |
| 9. C61×#2253 | C2 | semidirect |
| 130. #2253 | D61 | semidirect |
| 167. C61 | #33919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458186 | 2 |
| #21448029 | 2 |
| #21448023 | 2 |
| #21447980 | 2 |
| #21447928 | 2 |
| C4×Dic488 | 2 |
| #21447652 | 2 |
| #21447606 | 2 |
| C61×#2253 | 2 |
| #33919 | 61 |