Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
835 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 835 conjugacy classes of subgroups — too many to draw. Only its 142 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×#5748 | C2 | semidirect |
| 2. C3×#5524 | C2 | semidirect |
| 3. C3×#5126 | C2 | semidirect |
| 4. C3×#5005 | C2 | semidirect |
| 5. C32×H(3,ℤ/4) | C2 | semidirect |
| 7. #68703 | C3 | direct (N × H) |
| 25. #5748 | C2×C3 | semidirect |
| 26. #5524 | C2×C3 | semidirect |
| 29. #5126 | C2×C3 | semidirect |
| 30. #5005 | C2×C3 | semidirect |
| 32. C3×H(3,ℤ/4) | D3 | semidirect |
| 33. C3×H(3,ℤ/4) | C2×C3 | semidirect |
| 43. C2×C3×D12 | D4 | semidirect |
| 49. C2×C3×Dic6 | D4 | semidirect |
| 51. C2×C32×C8 | D4 | semidirect |
| 54. C32×C42 | D4 | semidirect |
| 127. H(3,ℤ/4) | C3×D3 | semidirect |
| 154. C2×D12 | C3×D4 | semidirect |
| 160. C2×Dic6 | C3×D4 | semidirect |
| 170. C2×C3×C8 | D12 | semidirect |
| 171. C2×C3×C8 | C3×D4 | semidirect |
| 182. C3×C42 | D12 | semidirect |
| 183. C3×C42 | C3×D4 | semidirect |
| 311. C2×C8 | C3×D12 | semidirect |
| 317. C42 | C3×D12 | semidirect |
| 357. C32 | #2010 | semidirect |
| 415. C3 | #68703 | direct (N × H) |
| 416. C3 | C3×#2010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5748 | 2 |
| C3×#5524 | 2 |
| C3×#5126 | 2 |
| C3×#5005 | 2 |
| C32×H(3,ℤ/4) | 2 |
| C3×#2010 | 3 |
| #68703 | 3 |