Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
462 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 108 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. #21462020 | C2 | semidirect |
| 2. D61⋊#334 | C2 | semidirect |
| 3. #21460778 | C2 | semidirect |
| 4. #21460777 | C2 | semidirect |
| 8. #16840651 | C22 | semidirect |
| 11. #16840623 | C22 | semidirect |
| 33. D8×D61 | C8 | semidirect |
| 75. D8×C61 | C2×C8 | semidirect |
| 93. D488 | C2×C8 | semidirect |
| 163. D61 | #1333 | semidirect |
| 181. C61 | C2×#1333 | semidirect |
| 235. D8 | D61⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462020 | 2 |
| D61⋊#334 | 2 |
| #21460778 | 2 |
| #21460777 | 2 |
| C4×D8×D61 | 2 |
| C2×#1333 | 61 |