Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2142 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2142 conjugacy classes of subgroups — too many to draw. Only its 747 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. C2×#16840131 | C2 | direct (N × H) |
| 14. #16840131 | C22 | direct (N × H) |
| 79. C22×C61 | #491 | semidirect |
| 93. C2×C61 | C2×#491 | semidirect |
| 109. C61 | C22×#491 | semidirect |
| 169. C22 | #16840131 | direct (N × H) |
| 178. C2 | C2×#16840131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14519777 | 2 |
| C22×#14519769 | 2 |
| C2×#16840131 | 2 |
| C22×#14519702 | 2 |
| C22×#97×C61 | 2 |
| C22×#491 | 61 |