Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
342 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 7. #16840657 | C4 | semidirect |
| 9. #16840638 | C4 | semidirect |
| 165. C61 | #7259 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840657 | 2 |
| C2×#16840638 | 2 |
| #21445845 | 2 |
| #7259 | 61 |