Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1074 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 219 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×#16840141 | C2 | semidirect |
| 2. C2×#16840052 | C2 | semidirect |
| 3. #21444964 | C2 | direct (N × H) |
| 4. C2×#16839511 | C2 | semidirect |
| 5. C2×D4⋊#92418 | C2 | semidirect |
| 10. #16840141 | C22 | semidirect |
| 12. #16840052 | C22 | semidirect |
| 17. #16839511 | C22 | semidirect |
| 18. D4⋊#92418 | C22 | semidirect |
| 159. C2×C61 | #1634 | semidirect |
| 182. C61 | C2×#1634 | semidirect |
| 308. C2 | #21444964 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840141 | 2 |
| C2×#16840052 | 2 |
| #21444964 | 2 |
| C2×#16839511 | 2 |
| C2×D4⋊#92418 | 2 |
| C2×C61×#555 | 2 |
| C2×#1634 | 61 |