Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
330 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 330 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 |
|---|---|---|
| 2. C4×#14519716 | C2 | semidirect |
| 3. #21444576 | C2 | semidirect |
| 4. #21443784 | C2 | semidirect |
| 5. #21443782 | C2 | semidirect |
| 6. #21443780 | C2 | semidirect |
| 7. C61×#1331 | C2 | semidirect |
| 156. #1331 | D61 | semidirect |
| 181. C61 | #11674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456387 | 2 |
| C4×#14519716 | 2 |
| #21444576 | 2 |
| #21443784 | 2 |
| #21443782 | 2 |
| #21443780 | 2 |
| C61×#1331 | 2 |
| #11674 | 61 |