Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
470 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 118 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. C4×D61⋊C16 | C2 | semidirect |
| 2. D61⋊#335 | C2 | semidirect |
| 3. #21460774 | C2 | semidirect |
| 4. #21460773 | C2 | semidirect |
| 8. #16840648 | C22 | semidirect |
| 11. #16840625 | C22 | semidirect |
| 33. D8×D61 | C8 | semidirect |
| 76. D8×C61 | C2×C8 | semidirect |
| 94. D488 | C2×C8 | semidirect |
| 168. D61 | #1331 | semidirect |
| 186. C61 | C2×#1331 | semidirect |
| 241. D8 | D61⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D61⋊C16 | 2 |
| D61⋊#335 | 2 |
| #21460774 | 2 |
| #21460773 | 2 |
| C4×D8×D61 | 2 |
| C2×#1331 | 61 |