Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
470 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 115 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. #21445848 | C2 | semidirect |
| 3. #21443829 | C2 | semidirect |
| 4. C2×C61×C22⋊C16 | C2 | semidirect |
| 5. C22×D488 | C4 | semidirect |
| 9. #16839998 | C4 | semidirect |
| 12. C2×#14519711 | C4 | semidirect |
| 15. #16839525 | C22 | semidirect |
| 19. C61×C22⋊C16 | C22 | semidirect |
| 154. C2×C22⋊C16 | D61 | semidirect |
| 178. C22⋊C16 | C2×D61 | semidirect |
| 180. C61 | #11886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16839998 | 2 |
| #21445848 | 2 |
| #21443829 | 2 |
| C2×C61×C22⋊C16 | 2 |
| #11886 | 61 |