Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#16839578 | C2 | semidirect |
| 5. #21443934 | C2 | semidirect |
| 6. #21443933 | C2 | semidirect |
| 7. C2×C61×#362 | C2 | semidirect |
| 161. C2×#362 | D61 | semidirect |
| 188. C61 | #13078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458921 | 2 |
| #21455470 | 2 |
| C2×#16839578 | 2 |
| #21445866 | 2 |
| #21443934 | 2 |
| #21443933 | 2 |
| C2×C61×#362 | 2 |
| #13078 | 61 |