Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
312 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 71 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. #10589388 | C2 | semidirect |
| 5. #10589387 | C2 | semidirect |
| 6. #10589315 | C2 | semidirect |
| 7. #10589313 | C2 | semidirect |
| 22. C3×Q64 | D3 | semidirect |
| 64. Q64 | C3⋊D3 | semidirect |
| 129. C32 | #2264 | semidirect |
| 151. C3 | #69384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592618 | 2 |
| C3⋊D3×Q32 | 2 |
| C32×Q64 | 2 |
| #10589388 | 2 |
| #10589387 | 2 |
| #10589315 | 2 |
| #10589313 | 2 |
| #69384 | 3 |