Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1198 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 216 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. C2×D61⋊#101 | C2 | semidirect |
| 2. #21462115 | C2 | direct (N × H) |
| 3. C2×#16840673 | C2 | semidirect |
| 4. C2×#16840670 | C2 | semidirect |
| 8. D61⋊#101 | C22 | semidirect |
| 11. #16840673 | C22 | semidirect |
| 12. #16840670 | C22 | semidirect |
| 223. C2×C61 | #2133 | semidirect |
| 245. C61 | C2×#2133 | semidirect |
| 439. C2 | #21462115 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D61⋊#101 | 2 |
| #21462115 | 2 |
| C2×#16840673 | 2 |
| C2×#16840670 | 2 |
| C2×#16840332 | 2 |
| C2×#2133 | 61 |