Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
466 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 466 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 |
|---|---|---|
| 2. C2×#16839884 | C2 | semidirect |
| 3. #21447548 | C2 | semidirect |
| 4. #21446710 | C2 | semidirect |
| 5. #21443932 | C2 | semidirect |
| 6. #21443902 | C2 | semidirect |
| 7. C61×#2148 | C2 | semidirect |
| 11. #16840202 | C4 | semidirect |
| 13. #16840197 | C4 | semidirect |
| 178. #2148 | D61 | semidirect |
| 210. C61 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458953 | 2 |
| C2×#16839884 | 2 |
| #21447548 | 2 |
| #21446710 | 2 |
| #21443932 | 2 |
| #21443902 | 2 |
| C61×#2148 | 2 |
| #13024 | 61 |