Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1250 conjugacy classes of subgroups; only the 328 normal subgroups are shown.
This group has 1250 conjugacy classes of subgroups — too many to draw. Only its 328 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 |
|---|---|---|
| 2. #21461557 | C2 | semidirect |
| 3. #21461553 | C2 | semidirect |
| 4. #21461549 | C2 | semidirect |
| 9. D61⋊(C22⋊C8) | C4 | semidirect |
| 11. C2×#14519832 | C22 | semidirect |
| 12. C2×C4×#92420 | C22 | semidirect |
| 13. #16840628 | C22 | semidirect |
| 146. C61 | #20528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D61⋊(C22⋊C8) | 2 |
| #21461557 | 2 |
| #21461553 | 2 |
| #21461549 | 2 |
| #21448199 | 2 |
| #20528 | 61 |