Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
785 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 785 conjugacy classes of subgroups — too many to draw. Only its 188 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 |
|---|---|---|
| 3. C3×#4878 | C2 | semidirect |
| 4. #10590873 | C2 | semidirect |
| 8. #10590414 | C2 | semidirect |
| 36. #4878 | D3 | semidirect |
| 222. C3⋊D3 | #499 | semidirect |
| 268. C32 | C2×#499 | semidirect |
| 307. C3 | D3×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594482 | 2 |
| C3⋊D3×#107 | 2 |
| C3×#4878 | 2 |
| #10590873 | 2 |
| #10590687 | 2 |
| C8×#624 | 2 |
| #10590575 | 2 |
| #10590414 | 2 |
| D3×#499 | 3 |