Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
544 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21462547 | C2 | semidirect |
| 2. #21461943 | C2 | semidirect |
| 3. #21461317 | C2 | semidirect |
| 4. #21461144 | C2 | semidirect |
| 5. #21460710 | C2 | semidirect |
| 6. #21460658 | C2 | semidirect |
| 134. C2×#92420 | D8 | semidirect |
| 286. C61 | #9049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462547 | 2 |
| #21461943 | 2 |
| #21461317 | 2 |
| #21461144 | 2 |
| #21460710 | 2 |
| #21460658 | 2 |
| #21455814 | 2 |
| #9049 | 61 |