Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #21446758 | C2 | semidirect |
| 5. #21444247 | C2 | semidirect |
| 6. #21443663 | C2 | semidirect |
| 7. C61×#1301 | C2 | semidirect |
| 116. C2×#92418 | SD16 | semidirect |
| 185. #1301 | D61 | semidirect |
| 214. C61 | #9047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455851 | 2 |
| #21454536 | 2 |
| #21446758 | 2 |
| #21444469 | 2 |
| #21444247 | 2 |
| #21443663 | 2 |
| C61×#1301 | 2 |
| #9047 | 61 |