Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
293 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 293 conjugacy classes of subgroups — too many to draw. Only its 94 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 |
|---|---|---|
| 9. #69218 | C3 | direct (N × H) |
| 242. C32 | #2245 | semidirect |
| 276. C3 | #69218 | direct (N × H) |
| 277. C3 | C3×#2245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5183 | 2 |
| C3×#4878 | 2 |
| C32×#358 | 2 |
| C3×#4564 | 2 |
| C3×#4503 | 2 |
| C3×#4502 | 2 |
| C3×#4492 | 2 |
| C3×#2245 | 3 |
| #69218 | 3 |