Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
400 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 114 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. #21461032 | C2 | semidirect |
| 4. #21461022 | C2 | semidirect |
| 5. #21460659 | C2 | semidirect |
| 6. #21460659 | C2 | semidirect |
| 199. C61 | #8158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461052 | 2 |
| #21461032 | 2 |
| #21461022 | 2 |
| #21460659 | 2 |
| C2×#16839822 | 2 |
| #8158 | 61 |