Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 305 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 4. #73123 | C3 | direct (N × H) |
| 7. C3×#131⋊C3 | C4 | semidirect |
| 8. C3×GU(2,𝔽3) | C4 | semidirect |
| 9. C3×#859 | C4 | semidirect |
| 33. C3×#131 | Dic3 | semidirect |
| 41. #131⋊C3 | C3×C4 | semidirect |
| 42. GU(2,𝔽3) | C3×C4 | semidirect |
| 43. #859 | C3×C4 | semidirect |
| 105. #131 | C3×Dic3 | semidirect |
| 230. C3 | #73123 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131⋊C3 | 2 |
| C3×#5424 | 2 |
| C2×C3×GU(2,𝔽3) | 2 |
| #73123 | 3 |
| C3×#1765 | 3 |
| C3×#815 | 4 |