Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
188 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 8. #65707 | C3 | direct (N × H) |
| 39. C3×#170 | Q8 | semidirect |
| 90. #170 | C3×Q8 | semidirect |
| 133. C3×C5 | #446 | semidirect |
| 161. C5 | C3×#446 | semidirect |
| 171. C3 | #65707 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4033 | 2 |
| C3×#4004 | 2 |
| C3×#4002 | 2 |
| C3×C4⋊#170 | 2 |
| C3×C4×#170 | 2 |
| #65707 | 3 |
| C3×#446 | 5 |