Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1198 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 224 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. #21462121 | C2 | direct (N × H) |
| 3. C2×#16840672 | C2 | semidirect |
| 10. #16840672 | C22 | semidirect |
| 189. C2×C61 | #2135 | semidirect |
| 208. C61 | C2×#2135 | semidirect |
| 373. C2 | #21462121 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840748 | 2 |
| #21462121 | 2 |
| C2×#16840672 | 2 |
| C2×#16840336 | 2 |
| C2×#2135 | 61 |