Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
220 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 83 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. #21444716 | C2 | semidirect |
| 3. #21443891 | C2 | semidirect |
| 4. #21443783 | C2 | semidirect |
| 6. #21443735 | C2 | semidirect |
| 66. C16×C61 | M16 | semidirect |
| 128. C61 | #12084 | semidirect |
| 173. C16 | #11758194 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21444716 | 2 |
| #21444704 | 2 |
| #21443891 | 2 |
| #21443783 | 2 |
| #21443780 | 2 |
| #21443735 | 2 |
| C4×SD32×C61 | 2 |
| #12084 | 61 |