Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
434 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 98 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. D61⋊#334 | C2 | semidirect |
| 3. #21460832 | C2 | semidirect |
| 4. #21460831 | C2 | semidirect |
| 8. #16840683 | C22 | semidirect |
| 10. #16840624 | C22 | semidirect |
| 174. D61 | #1360 | semidirect |
| 192. C61 | C2×#1360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊(C4⋊C16) | 2 |
| D61⋊#334 | 2 |
| #21460832 | 2 |
| #21460831 | 2 |
| #495×D61 | 2 |
| C2×#1360 | 61 |