Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
580 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 219 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 |
|---|---|---|
| 3. #91833 | C2 | direct (N × H) |
| 30. C2×Dic15 | Q8 | semidirect |
| 56. Dic15 | C2×Q8 | semidirect |
| 83. C2×C3×C5 | C4⋊Q8 | semidirect |
| 114. C3×C5 | C2×C4⋊Q8 | semidirect |
| 122. C2×C5 | #944 | semidirect |
| 136. C2×C3 | #4090 | semidirect |
| 139. C5 | C2×#944 | semidirect |
| 147. C3 | C2×#4090 | semidirect |
| 148. C2 | #91833 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C5×Q8 | 2 |
| C22×Dic30 | 2 |
| #91833 | 2 |
| C2×#6712 | 2 |
| C2×C4×Dic15 | 2 |
| C2×#4090 | 3 |
| C2×#944 | 5 |