Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
610 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. #21446659 | C2 | semidirect |
| 3. #21444578 | C2 | semidirect |
| 4. #21444486 | C2 | semidirect |
| 5. C8×M16×C61 | C2 | semidirect |
| 60. M16×C61 | D8 | semidirect |
| 99. C8×C61 | #100 | semidirect |
| 121. C8×M16 | D61 | semidirect |
| 141. C61 | #9802 | semidirect |
| 185. M16 | D488 | semidirect |
| 222. C8 | #14519693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840139 | 2 |
| #21446659 | 2 |
| #21444578 | 2 |
| #21444486 | 2 |
| C8×M16×C61 | 2 |
| #9802 | 61 |