Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
444 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 3. #21461028 | C2 | semidirect |
| 4. C8×#11758217 | C2 | semidirect |
| 5. #21460703 | C2 | semidirect |
| 6. #21460703 | C2 | semidirect |
| 214. C61 | #8245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461322 | 2 |
| #21461273 | 2 |
| #21461028 | 2 |
| C8×#11758217 | 2 |
| #21460703 | 2 |
| #21454527 | 2 |
| #8245 | 61 |