Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
614 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 230 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. #21462205 | C2 | semidirect |
| 2. #21462176 | C2 | semidirect |
| 3. #21462047 | C2 | semidirect |
| 5. C2×#14519852 | C22 | semidirect |
| 6. C4⋊#11758187 | C22 | semidirect |
| 7. #16840657 | C22 | semidirect |
| 9. C4×#11758187 | C22 | semidirect |
| 69. C2×C4×C61 | M32 | semidirect |
| 120. C61 | #33489 | semidirect |
| 179. C2×C4 | #14519852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462205 | 2 |
| #21462176 | 2 |
| #21462047 | 2 |
| C2×#16839827 | 2 |
| #33489 | 61 |