Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
936 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 148 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. C2×#16840661 | C2 | semidirect |
| 2. #21462046 | C2 | semidirect |
| 3. C2×C22⋊#11758187 | C2 | semidirect |
| 5. C2×#14519851 | C22 | semidirect |
| 6. C22×#11758187 | C22 | semidirect |
| 165. C22×C61 | #350 | semidirect |
| 206. C61 | #12683 | semidirect |
| 353. C22 | #16840661 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840661 | 2 |
| #21462046 | 2 |
| C2×C22⋊#11758187 | 2 |
| C22×#14519785 | 2 |
| #12683 | 61 |