Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
216 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 6. #65138 | C3 | direct (N × H) |
| 52. C3×C4×C5 | Q16 | semidirect |
| 100. C4×C5 | C3×Q16 | semidirect |
| 116. C3×C5 | #462 | semidirect |
| 122. C3×C4 | Dic20 | semidirect |
| 142. C5 | C3×#462 | semidirect |
| 148. C4 | C3×Dic20 | semidirect |
| 151. C3 | #65138 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic20 | 2 |
| C3×#4015 | 2 |
| C3×C4×Dic10 | 2 |
| C3×C5×C4⋊C8 | 2 |
| C3×#3948 | 2 |
| #65138 | 3 |
| C3×#462 | 5 |