Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #21444413 | C2 | semidirect |
| 4. #21444241 | C2 | semidirect |
| 6. C8×#11758194 | C2 | semidirect |
| 7. C4×#108×C61 | C2 | semidirect |
| 172. C4×#108 | D61 | semidirect |
| 206. C61 | #9723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456378 | 2 |
| #21444413 | 2 |
| #21444410 | 2 |
| #21444241 | 2 |
| #21444237 | 2 |
| C8×#11758194 | 2 |
| C4×#108×C61 | 2 |
| #9723 | 61 |