Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
361 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 361 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 |
|---|---|---|
| 1. C3×#5183 | C2 | semidirect |
| 5. C32×#358 | C2 | semidirect |
| 6. C3×Dic3⋊C16 | C2 | semidirect |
| 7. C3×#4492 | C2 | semidirect |
| 9. #69234 | C3 | direct (N × H) |
| 27. #5183 | C2×C3 | semidirect |
| 34. C3×#358 | D3 | semidirect |
| 35. C3×#358 | C2×C3 | semidirect |
| 36. Dic3⋊C16 | C2×C3 | semidirect |
| 37. #4492 | C2×C3 | semidirect |
| 111. #358 | C3×D3 | semidirect |
| 168. C3×Dic3 | SD32 | semidirect |
| 273. Dic3 | C3×SD32 | semidirect |
| 274. C32 | #2208 | semidirect |
| 315. C3 | #69234 | direct (N × H) |
| 316. C3 | C3×#2208 | 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×#828 | 2 |
| C2×C3×#800 | 2 |
| C3×#4872 | 2 |
| C32×#358 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#4492 | 2 |
| C3×#2208 | 3 |
| #69234 | 3 |