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. #10589386 | C2 | semidirect |
| 4. C3×#4520 | C2 | semidirect |
| 5. #10589076 | C2 | semidirect |
| 6. #10589075 | C2 | semidirect |
| 7. #10589068 | C2 | semidirect |
| 32. #4520 | D3 | semidirect |
| 190. C32 | #2264 | semidirect |
| 218. C3 | #69381 | semidirect |
| 219. C3 | #71510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4912 | 2 |
| D3×Dic24 | 2 |
| #10589386 | 2 |
| C3×#4520 | 2 |
| #10589076 | 2 |
| #10589075 | 2 |
| #10589068 | 2 |
| #71510 | 3 |
| #69381 | 3 |