Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
878 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 1. #21462141 | C2 | semidirect |
| 2. #21462129 | C2 | semidirect |
| 3. #21462056 | C2 | semidirect |
| 4. #21461701 | C2 | semidirect |
| 20. C2×#14519800 | C4 | semidirect |
| 22. C2×#14519799 | C4 | semidirect |
| 23. C2×Q16×D61 | C4 | semidirect |
| 26. C22×Q16×C61 | C4 | semidirect |
| 241. C22×Q16 | #6923 | semidirect |
| 251. C61 | #12742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462141 | 2 |
| #21462129 | 2 |
| #21462056 | 2 |
| #21461701 | 2 |
| C2×#16840575 | 2 |
| #12742 | 61 |