Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
296 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 85 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. #21445992 | C2 | semidirect |
| 4. #21443932 | C2 | semidirect |
| 5. #21443931 | C2 | semidirect |
| 6. #21443898 | C2 | semidirect |
| 160. C61 | #13486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447568 | 2 |
| #21446713 | 2 |
| #21445992 | 2 |
| #21443932 | 2 |
| #21443931 | 2 |
| #21443898 | 2 |
| C61×#2148 | 2 |
| #13486 | 61 |