Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
369 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 369 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 |
|---|---|---|
| 1. C3×#5191 | C2 | semidirect |
| 2. C2×C3×#828 | C2 | semidirect |
| 4. C3×#4872 | C2 | semidirect |
| 5. C32×#358 | C2 | semidirect |
| 6. C3×Dic3⋊C16 | C2 | semidirect |
| 7. C3×#4491 | C2 | semidirect |
| 9. #69235 | C3 | direct (N × H) |
| 27. #5191 | C2×C3 | semidirect |
| 28. C2×#828 | C2×C3 | semidirect |
| 30. #4872 | C2×C3 | semidirect |
| 33. C3×#358 | D3 | semidirect |
| 34. C3×#358 | C2×C3 | semidirect |
| 36. Dic3⋊C16 | C2×C3 | semidirect |
| 37. #4491 | C2×C3 | semidirect |
| 110. #358 | C3×D3 | semidirect |
| 281. C32 | #2210 | semidirect |
| 326. C3 | #69235 | direct (N × H) |
| 327. C3 | C3×#2210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5191 | 2 |
| C2×C3×#828 | 2 |
| C2×C3×D48 | 2 |
| C3×#4872 | 2 |
| C32×#358 | 2 |
| C3×Dic3⋊C16 | 2 |
| C3×#4491 | 2 |
| C3×#2210 | 3 |
| #69235 | 3 |