Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
424 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 230 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. #66056 | C3 | direct (N × H) |
| 30. C3×Dic10 | Q8 | semidirect |
| 70. Dic10 | C3×Q8 | semidirect |
| 102. C3×C5 | Q82 | semidirect |
| 121. C5 | C3×Q82 | semidirect |
| 128. C3 | #66056 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C4⋊Q8 | 2 |
| C3×#4090 | 2 |
| C3×#4034 | 2 |
| C3×#4033 | 2 |
| C3×C4×Dic10 | 2 |
| #66056 | 3 |
| C3×Q82 | 5 |