Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 866 conjugacy classes of subgroups — too many to draw. Only its 251 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×#16840160 | C2 | semidirect |
| 2. C2×#16840114 | C2 | semidirect |
| 4. #21445418 | C2 | direct (N × H) |
| 5. C2×C8×#92418 | C2 | semidirect |
| 9. #16840160 | C22 | semidirect |
| 11. #16840114 | C22 | semidirect |
| 18. C8×#92418 | C22 | semidirect |
| 129. C2×C61 | #1708 | semidirect |
| 150. C61 | C2×#1708 | semidirect |
| 248. C2 | #21445418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840160 | 2 |
| C2×#16840114 | 2 |
| C2×#16840108 | 2 |
| #21445418 | 2 |
| C2×C8×#92418 | 2 |
| C2×C61×#492 | 2 |
| C2×#1708 | 61 |