Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
304 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 71 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. Q16×Dic122 | C2 | semidirect |
| 4. #21443876 | C2 | semidirect |
| 5. #21443797 | C2 | semidirect |
| 6. #21443783 | C2 | semidirect |
| 61. Q16×C61 | SD16 | semidirect |
| 103. Dic122 | SD32 | semidirect |
| 152. C61 | #12354 | semidirect |
| 189. Q16 | #11758200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×Dic122 | 2 |
| #21448042 | 2 |
| #21445176 | 2 |
| #21443876 | 2 |
| #21443797 | 2 |
| #21443783 | 2 |
| C61×#2207 | 2 |
| #12354 | 61 |