Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
224 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 56 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. D3×Dic24 | C2 | semidirect |
| 3. #10589315 | C2 | semidirect |
| 4. C3×Dic48 | C2 | semidirect |
| 5. C3×#4447 | C2 | semidirect |
| 6. #10589076 | C2 | semidirect |
| 7. #10589074 | C2 | semidirect |
| 30. Dic48 | D3 | semidirect |
| 35. #4447 | D3 | semidirect |
| 190. C32 | #2264 | semidirect |
| 218. C3 | #69374 | semidirect |
| 219. C3 | #69384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590243 | 2 |
| D3×Dic24 | 2 |
| #10589315 | 2 |
| C3×Dic48 | 2 |
| C3×#4447 | 2 |
| #10589076 | 2 |
| #10589074 | 2 |
| #69384 | 3 |
| #69374 | 3 |