Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1342 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 232 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. #21462408 | C2 | semidirect |
| 2. #21461096 | C2 | semidirect |
| 3. #21461076 | C2 | semidirect |
| 4. #21461056 | C2 | semidirect |
| 120. C2×C4×C61 | #131 | semidirect |
| 188. C61 | #17419 | semidirect |
| 300. C2×C4 | #14519865 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462408 | 2 |
| #21461096 | 2 |
| #21461076 | 2 |
| #21461056 | 2 |
| C2×#16840434 | 2 |
| #17419 | 61 |