Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
600 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 82 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. #21462383 | C2 | semidirect |
| 2. #21461158 | C2 | semidirect |
| 3. #21461071 | C2 | semidirect |
| 4. #21460678 | C2 | semidirect |
| 36. C4×#92420 | D4 | semidirect |
| 214. C61 | #9492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462383 | 2 |
| #21461158 | 2 |
| #21461071 | 2 |
| #21460678 | 2 |
| #21451378 | 2 |
| #9492 | 61 |