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 |
|---|---|---|
| 2. #21462011 | C2 | semidirect |
| 4. C2×#16840622 | C2 | semidirect |
| 5. #21460710 | C2 | semidirect |
| 6. #21460663 | C2 | semidirect |
| 120. #11758217 | SD16 | semidirect |
| 272. C61 | #9267 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462563 | 2 |
| #21462011 | 2 |
| #21461331 | 2 |
| C2×#16840622 | 2 |
| #21460710 | 2 |
| #21460663 | 2 |
| #21456742 | 2 |
| #9267 | 61 |