Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
472 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 151 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. #21458960 | C2 | semidirect |
| 2. #21448134 | C2 | semidirect |
| 3. #21448128 | C2 | semidirect |
| 4. C2×D1952 | C2 | semidirect |
| 5. C61×#2258 | C2 | semidirect |
| 8. #16840194 | C22 | semidirect |
| 9. C2×D976 | C22 | semidirect |
| 10. Dic976 | C22 | semidirect |
| 11. #16839601 | C22 | semidirect |
| 12. D1952 | C22 | semidirect |
| 13. D1952 | C22 | semidirect |
| 15. C61×M64 | C22 | semidirect |
| 16. C2×C32×C61 | C22 | semidirect |
| 65. #2258 | D61 | semidirect |
| 78. M64 | C2×D61 | semidirect |
| 79. C2×C32 | C2×D61 | semidirect |
| 80. C61 | #33982 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458960 | 2 |
| #21448134 | 2 |
| #21448128 | 2 |
| C2×D1952 | 2 |
| C61×#2258 | 2 |
| #33982 | 61 |