Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
510 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 124 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×#16840652 | C2 | semidirect |
| 4. #21460859 | C2 | semidirect |
| 14. #16840657 | C4 | semidirect |
| 15. C22⋊#11758187 | C4 | semidirect |
| 19. C22⋊#11758185 | C4 | semidirect |
| 20. #16839541 | C4 | semidirect |
| 21. C61×C22⋊C16 | C4 | semidirect |
| 36. C2×#11758187 | C2×C4 | semidirect |
| 51. C2×#11758185 | C2×C4 | semidirect |
| 53. C2×C16×C61 | C2×C4 | semidirect |
| 139. C22×C61 | #347 | semidirect |
| 147. C2×D61 | #347 | semidirect |
| 184. C22⋊C16 | #6923 | semidirect |
| 186. C61 | #12605 | semidirect |
| 214. C2×C16 | C2×#6923 | semidirect |
| 312. C22 | #16840652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519831 | 2 |
| #21462047 | 2 |
| C2×#16840652 | 2 |
| #21460859 | 2 |
| #21447428 | 2 |
| #12605 | 61 |