Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
466 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 120 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. #21462151 | C2 | semidirect |
| 2. C2×#16840659 | C2 | semidirect |
| 3. C4×#14519851 | C2 | semidirect |
| 23. #14519851 | D4 | semidirect |
| 124. C4×C61 | #349 | semidirect |
| 154. C61 | #13194 | semidirect |
| 258. C4 | #16840659 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462151 | 2 |
| C2×#16840659 | 2 |
| C4×#14519851 | 2 |
| C2×#16839839 | 2 |
| #13194 | 61 |