Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
384 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 80 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. #21461381 | C2 | semidirect |
| 2. #21461283 | C2 | semidirect |
| 4. #21461093 | C2 | semidirect |
| 6. #21461028 | C2 | semidirect |
| 205. C61 | #9790 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461381 | 2 |
| #21461283 | 2 |
| #21461278 | 2 |
| #21461093 | 2 |
| #21461089 | 2 |
| #21461028 | 2 |
| C2×#16840115 | 2 |
| #9790 | 61 |