Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 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. #21447727 | C2 | semidirect |
| 2. #21445176 | C2 | semidirect |
| 3. #21443893 | C2 | semidirect |
| 4. #21443865 | C2 | semidirect |
| 50. C16×C61 | SD16 | semidirect |
| 100. C61 | #12442 | semidirect |
| 135. C16 | #11758200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447727 | 2 |
| #21445176 | 2 |
| #21443893 | 2 |
| #21443865 | 2 |
| C61×#2246 | 2 |
| #12442 | 61 |