Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 422 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. D61⋊(C4⋊C16) | C2 | semidirect |
| 2. #21462020 | C2 | semidirect |
| 3. #21460772 | C2 | semidirect |
| 4. #21460771 | C2 | semidirect |
| 9. C4⋊#11758187 | C22 | semidirect |
| 11. #16840650 | C22 | semidirect |
| 168. D61 | #1330 | semidirect |
| 186. C61 | C2×#1330 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊(C4⋊C16) | 2 |
| #21462020 | 2 |
| #21460772 | 2 |
| #21460771 | 2 |
| #436×D61 | 2 |
| C2×#1330 | 61 |