Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
226 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 88 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. #21460845 | C2 | semidirect |
| 4. #21460844 | C2 | semidirect |
| 56. C16×C61 | M16 | semidirect |
| 58. #11758185 | M16 | semidirect |
| 111. C61 | #12019 | semidirect |
| 151. C16 | #11758217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461379 | 2 |
| #21461373 | 2 |
| #21460845 | 2 |
| #21460844 | 2 |
| C2×#16839537 | 2 |
| #12019 | 61 |