Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
224 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 50 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. #10590240 | C2 | semidirect |
| 3. #10589313 | C2 | semidirect |
| 4. C3×Dic48 | C2 | semidirect |
| 5. C3×#4449 | C2 | semidirect |
| 6. #10589075 | C2 | semidirect |
| 7. #10589072 | C2 | semidirect |
| 31. Dic48 | D3 | semidirect |
| 32. #4449 | D3 | semidirect |
| 190. C32 | #2264 | semidirect |
| 218. C3 | #69381 | semidirect |
| 219. C3 | #69384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590244 | 2 |
| #10590240 | 2 |
| #10589313 | 2 |
| C3×Dic48 | 2 |
| C3×#4449 | 2 |
| #10589075 | 2 |
| #10589072 | 2 |
| #69384 | 3 |
| #69381 | 3 |