Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
134 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 41 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. Q64×D61 | C2 | semidirect |
| 3. #21444035 | C2 | semidirect |
| 4. #21444034 | C2 | semidirect |
| 5. #21444033 | C2 | semidirect |
| 6. C64×D61 | C2 | semidirect |
| 7. C61×SD128 | C2 | semidirect |
| 10. Dic976 | C22 | semidirect |
| 15. #16839481 | C22 | semidirect |
| 16. C61×Q64 | C22 | semidirect |
| 18. C61×C64 | C22 | semidirect |
| 66. SD128 | D61 | direct (N × H) |
| 71. D61 | SD128 | direct (N × H) |
| 76. Q64 | C2×D61 | semidirect |
| 82. C64 | C2×D61 | semidirect |
| 83. C61 | C2×SD128 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q64×D61 | 2 |
| D32×D61 | 2 |
| #21444035 | 2 |
| #21444034 | 2 |
| #21444033 | 2 |
| C64×D61 | 2 |
| C61×SD128 | 2 |
| C2×SD128 | 61 |