Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
269 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 269 conjugacy classes of subgroups — too many to draw. Only its 60 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. #73126 | C3 | direct (N × H) |
| 6. C3×#131⋊C3 | C4 | semidirect |
| 27. C3×#131 | Dic3 | semidirect |
| 33. #131⋊C3 | C3×C4 | semidirect |
| 84. #131 | C3×Dic3 | semidirect |
| 198. C3 | #73126 | 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×#5426 | 2 |
| #73126 | 3 |
| C3×#1816 | 3 |
| C3×#818 | 4 |