Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
958 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 171 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. C2×#16840168 | C2 | semidirect |
| 3. #21445128 | C2 | direct (N × H) |
| 4. C2×#16839503 | C2 | semidirect |
| 16. #16840168 | C22 | semidirect |
| 20. #16839503 | C22 | semidirect |
| 172. C2×C61 | #1660 | semidirect |
| 197. C61 | C2×#1660 | semidirect |
| 334. C2 | #21445128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840512 | 2 |
| C2×#16840168 | 2 |
| #21445128 | 2 |
| C2×#16839503 | 2 |
| C2×#16839502 | 2 |
| C2×C61×#497 | 2 |
| C2×#1660 | 61 |