Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
223 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 70 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×D3×Q32 | C2 | semidirect |
| 3. C32×Q64 | C2 | semidirect |
| 4. C3×#4522 | C2 | semidirect |
| 5. C3×#4521 | C2 | semidirect |
| 6. C3×#4449 | C2 | semidirect |
| 7. C3×#4447 | C2 | semidirect |
| 9. #69384 | C3 | direct (N × H) |
| 24. D3×Q32 | C2×C3 | semidirect |
| 27. C3×Q64 | D3 | semidirect |
| 28. C3×Q64 | C2×C3 | semidirect |
| 32. #4522 | C2×C3 | semidirect |
| 33. #4521 | C2×C3 | semidirect |
| 34. #4449 | C2×C3 | semidirect |
| 35. #4447 | C2×C3 | semidirect |
| 87. Q64 | C3×D3 | semidirect |
| 190. C32 | #2264 | semidirect |
| 217. C3 | #69384 | direct (N × H) |
| 218. C3 | C3×#2264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4919 | 2 |
| C3×D3×Q32 | 2 |
| C32×Q64 | 2 |
| C3×#4522 | 2 |
| C3×#4521 | 2 |
| C3×#4449 | 2 |
| C3×#4447 | 2 |
| C3×#2264 | 3 |
| #69384 | 3 |