Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
222 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 86 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. Q8×#11758187 | C2 | semidirect |
| 3. #21460848 | C2 | semidirect |
| 4. Q8⋊#11758187 | C2 | semidirect |
| 6. #21460734 | C2 | semidirect |
| 70. Q8×C61 | M32 | semidirect |
| 128. C61 | #12056 | semidirect |
| 176. Q8 | #14519851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11758187 | 2 |
| #21462203 | 2 |
| #21460848 | 2 |
| Q8⋊#11758187 | 2 |
| D4⋊#11758187 | 2 |
| #21460734 | 2 |
| SD16×#92418 | 2 |
| #12056 | 61 |