Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
575 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 575 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 2. C3×#5119 | C2 | semidirect |
| 3. C3×#5006 | C2 | semidirect |
| 4. C3×#5002 | C2 | semidirect |
| 5. C32×H(3,ℤ/4) | C2 | semidirect |
| 7. #68698 | C3 | direct (N × H) |
| 25. #5119 | C2×C3 | semidirect |
| 26. #5006 | C2×C3 | semidirect |
| 27. #5002 | C2×C3 | semidirect |
| 29. C3×H(3,ℤ/4) | D3 | semidirect |
| 30. C3×H(3,ℤ/4) | C2×C3 | semidirect |
| 103. H(3,ℤ/4) | C3×D3 | semidirect |
| 277. C32 | #2053 | semidirect |
| 320. C3 | #68698 | direct (N × H) |
| 321. C3 | C3×#2053 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5748 | 2 |
| C3×#5119 | 2 |
| C3×#5006 | 2 |
| C3×#5002 | 2 |
| C32×H(3,ℤ/4) | 2 |
| C3×#2053 | 3 |
| #68698 | 3 |