Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
450 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 132 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×#16840660 | C2 | semidirect |
| 3. C2×C4×#11758187 | C2 | semidirect |
| 21. C2×#11758187 | D4 | semidirect |
| 96. C4×C61 | #350 | semidirect |
| 120. C61 | #13191 | semidirect |
| 199. C4 | #16840660 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462151 | 2 |
| C2×#16840660 | 2 |
| C2×C4×#11758187 | 2 |
| #21454531 | 2 |
| #13191 | 61 |