Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 88 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. #21462616 | C2 | semidirect |
| 3. #21461337 | C2 | semidirect |
| 5. #21460710 | C2 | semidirect |
| 6. #21460663 | C2 | semidirect |
| 119. #11758217 | SD16 | semidirect |
| 275. C61 | #9274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462616 | 2 |
| #21461961 | 2 |
| #21461337 | 2 |
| C2×#16840620 | 2 |
| #21460710 | 2 |
| #21460663 | 2 |
| #21456758 | 2 |
| #9274 | 61 |