Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
536 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 98 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. #21462684 | C2 | semidirect |
| 2. #21461120 | C2 | semidirect |
| 3. #21461120 | C2 | semidirect |
| 4. #21461060 | C2 | semidirect |
| 5. #21460659 | C2 | semidirect |
| 6. #21460645 | C2 | semidirect |
| 86. C2×D244 | M16 | semidirect |
| 100. C2×C8×C61 | M16 | semidirect |
| 221. C61 | #9093 | semidirect |
| 299. C2×C8 | #11758213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462684 | 2 |
| #21461120 | 2 |
| #21461060 | 2 |
| #21460659 | 2 |
| #21460645 | 2 |
| C2×#16839873 | 2 |
| #9093 | 61 |