Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 118 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×#16840653 | C2 | semidirect |
| 4. #21460859 | C2 | semidirect |
| 7. C2×#14519852 | C4 | semidirect |
| 10. C22×#11758187 | C4 | semidirect |
| 18. C22⋊#11758185 | C4 | semidirect |
| 19. #16839541 | C4 | semidirect |
| 20. C61×C22⋊C16 | C4 | semidirect |
| 78. #11758187 | C22⋊C4 | semidirect |
| 112. C22×C61 | #347 | semidirect |
| 150. C22⋊C16 | #6923 | semidirect |
| 153. C61 | #12616 | semidirect |
| 251. C22 | #16840653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519852 | 2 |
| C2×#16840653 | 2 |
| #21461555 | 2 |
| #21460859 | 2 |
| #21447428 | 2 |
| #12616 | 61 |