Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
610 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 125 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. #21444577 | C2 | semidirect |
| 4. #21444488 | C2 | semidirect |
| 5. #21444487 | C2 | semidirect |
| 6. M16×#92418 | C2 | semidirect |
| 7. C61×#1965 | C2 | semidirect |
| 89. M16×C61 | D8 | semidirect |
| 142. #92418 | #100 | semidirect |
| 165. #1965 | D61 | semidirect |
| 194. C61 | #9802 | semidirect |
| 261. M16 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840138 | 2 |
| #21446659 | 2 |
| #21444577 | 2 |
| #21444488 | 2 |
| #21444487 | 2 |
| M16×#92418 | 2 |
| C61×#1965 | 2 |
| #9802 | 61 |