Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
466 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 111 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. #21445536 | C2 | semidirect |
| 3. #21443832 | C2 | semidirect |
| 4. #21443829 | C2 | semidirect |
| 5. C2×C61×C22⋊C16 | C2 | semidirect |
| 6. C2×#14519799 | C4 | semidirect |
| 9. #16840003 | C4 | semidirect |
| 11. #16839998 | C4 | semidirect |
| 15. #16839800 | C4 | semidirect |
| 168. C2×C22⋊C16 | D61 | semidirect |
| 196. C61 | #11703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455400 | 2 |
| #21445536 | 2 |
| #21443832 | 2 |
| #21443829 | 2 |
| C2×C61×C22⋊C16 | 2 |
| #11703 | 61 |