Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
337 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 337 conjugacy classes of subgroups — too many to draw. Only its 98 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. #69236 | C3 | direct (N × H) |
| 165. C3×Dic3 | Q32 | semidirect |
| 263. Dic3 | C3×Q32 | semidirect |
| 264. C32 | #2209 | semidirect |
| 300. C3 | #69236 | direct (N × H) |
| 301. C3 | C3×#2209 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5183 | 2 |
| C2×C3×#829 | 2 |
| C2×C3×Dic24 | 2 |
| C3×#4873 | 2 |
| C32×#358 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#4492 | 2 |
| C3×#2209 | 3 |
| #69236 | 3 |