Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
296 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 61 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. #21448058 | C2 | semidirect |
| 3. #21445344 | C2 | semidirect |
| 4. #21443863 | C2 | semidirect |
| 5. #21443800 | C2 | semidirect |
| 6. #21443786 | C2 | semidirect |
| 7. C61×#2224 | C2 | semidirect |
| 144. #2224 | D61 | semidirect |
| 173. C61 | #12388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458905 | 2 |
| #21448058 | 2 |
| #21445344 | 2 |
| #21443863 | 2 |
| #21443800 | 2 |
| #21443786 | 2 |
| C61×#2224 | 2 |
| #12388 | 61 |