Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
218 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 31. Q16×C61 | C16 | semidirect |
| 45. #11758187 | Q16 | direct (N × H) |
| 87. C61 | C16×Q16 | semidirect |
| 103. Q16 | #11758187 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11758187 | 2 |
| #21460848 | 2 |
| Q8⋊#11758187 | 2 |
| C8×#11758187 | 2 |
| Q16×#92418 | 2 |
| C16×Q16 | 61 |