Finite Group DatabasebetaFinite Group DatabasebetaOrder 960.
168 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 2. C3×#4004 | C2 | semidirect |
| 3. #64925 | C3 | direct (N × H) |
| 11. #4004 | C2×C3 | semidirect |
| 79. C3×C5 | #331 | semidirect |
| 105. C5 | C3×#331 | semidirect |
| 114. C3 | #64925 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4086 | 2 |
| C3×#4004 | 2 |
| #64925 | 3 |
| C3×#331 | 5 |