Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
281 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 281 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 3. #83784 | C3 | semidirect |
| 6. C3×#131⋊C3 | C4 | semidirect |
| 27. C3×#131 | C3×C4 | semidirect |
| 35. #131⋊C3 | Dic3 | semidirect |
| 85. #131 | C3×Dic3 | semidirect |
| 196. C3 | #2912⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131⋊C3 | 2 |
| #5827⋊C3 | 2 |
| #83784 | 3 |
| #2912⋊C3 | 3 |
| C3×#817 | 4 |