Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
202 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 75 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. Q32×Dic61 | C2 | semidirect |
| 3. #21444021 | C2 | semidirect |
| 4. #21444000 | C2 | semidirect |
| 6. C32×Dic61 | C2 | semidirect |
| 18. C61×SD64 | C4 | semidirect |
| 32. Q32×C61 | C2×C4 | semidirect |
| 36. C32×C61 | C2×C4 | semidirect |
| 81. Dic61 | SD64 | direct (N × H) |
| 97. SD64 | Dic61 | direct (N × H) |
| 105. C61 | C4×SD64 | semidirect |
| 111. Q32 | C2×Dic61 | semidirect |
| 122. C32 | C2×Dic61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q32×Dic61 | 2 |
| D16×Dic61 | 2 |
| #21444021 | 2 |
| #21444000 | 2 |
| #21443997 | 2 |
| C32×Dic61 | 2 |
| C2×C61×SD64 | 2 |
| C4×SD64 | 61 |