Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
420 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 120 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×#16840652 | C2 | semidirect |
| 4. #21460859 | C2 | semidirect |
| 10. #16840657 | C4 | semidirect |
| 11. C22⋊#11758187 | C4 | semidirect |
| 16. C2×#14519716 | C4 | semidirect |
| 17. C2×#14519716 | C4 | semidirect |
| 20. C22×#11758185 | C4 | semidirect |
| 21. C22×C16×C61 | C4 | semidirect |
| 83. C16×C61 | C22⋊C4 | semidirect |
| 85. #11758185 | C22⋊C4 | semidirect |
| 117. C22×C61 | #347 | semidirect |
| 151. C22×C16 | #6923 | semidirect |
| 159. C61 | #12616 | semidirect |
| 223. C16 | C22⋊#6923 | semidirect |
| 261. C22 | #16840652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462047 | 2 |
| C2×#16840652 | 2 |
| #21461555 | 2 |
| #21460859 | 2 |
| C22×#14519716 | 2 |
| #12616 | 61 |