Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
249 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 249 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 |
|---|---|---|
| 1. C3⋊D3×Q32 | C2 | semidirect |
| 3. C3×#4522 | C2 | semidirect |
| 4. C3×#4521 | C2 | semidirect |
| 5. #10589076 | C2 | semidirect |
| 6. #10589073 | C2 | semidirect |
| 7. #10589069 | C2 | semidirect |
| 29. #4522 | D3 | semidirect |
| 30. #4521 | D3 | semidirect |
| 202. C32 | #2264 | semidirect |
| 230. C3 | #69381 | semidirect |
| 231. C3 | #69384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×Q32 | 2 |
| #10590244 | 2 |
| C3×#4522 | 2 |
| C3×#4521 | 2 |
| #10589076 | 2 |
| #10589073 | 2 |
| #10589069 | 2 |
| #69384 | 3 |
| #69381 | 3 |