Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
422 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 90 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×#5069 | C2 | semidirect |
| 3. C3×#4714 | C2 | semidirect |
| 4. C32×#330 | C2 | semidirect |
| 5. C3×#4464 | C2 | semidirect |
| 7. #68374 | C3 | direct (N × H) |
| 23. #5069 | C2×C3 | semidirect |
| 24. #4714 | C2×C3 | semidirect |
| 26. C3×#330 | D3 | semidirect |
| 27. C3×#330 | C2×C3 | semidirect |
| 29. #4464 | C2×C3 | semidirect |
| 86. #330 | C3×D3 | semidirect |
| 212. C32 | #1662 | semidirect |
| 244. C3 | #68374 | direct (N × H) |
| 245. C3 | C3×#1662 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5700 | 2 |
| C3×#5069 | 2 |
| C3×#4714 | 2 |
| C32×#330 | 2 |
| C3×#4464 | 2 |
| C3×#1662 | 3 |
| #68374 | 3 |