Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
410 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 128 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. #21462027 | C2 | semidirect |
| 4. #21460868 | C2 | semidirect |
| 10. #16840659 | C4 | semidirect |
| 11. #16840658 | C4 | semidirect |
| 18. C2×#14519716 | C4 | semidirect |
| 20. C22×#11758185 | C4 | semidirect |
| 21. C2×C16×D61 | C4 | semidirect |
| 23. C2×M32×C61 | C4 | semidirect |
| 145. C2×M32 | #6923 | semidirect |
| 157. C61 | #12613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462056 | 2 |
| #21462027 | 2 |
| #21461574 | 2 |
| #21460868 | 2 |
| C2×#16840180 | 2 |
| #12613 | 61 |