Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
223 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 223 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 |
|---|---|---|
| 1. C3×D3×Q32 | C2 | semidirect |
| 3. #10589388 | C2 | semidirect |
| 4. C3×#4521 | C2 | semidirect |
| 5. #10589076 | C2 | semidirect |
| 6. #10589072 | C2 | semidirect |
| 7. #10589068 | C2 | semidirect |
| 22. D3×Q32 | D3 | semidirect |
| 31. #4521 | D3 | semidirect |
| 190. C32 | #2264 | semidirect |
| 217. C3 | #69381 | semidirect |
| 218. C3 | #71493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D3×Q32 | 2 |
| #10590241 | 2 |
| #10589388 | 2 |
| C3×#4521 | 2 |
| #10589076 | 2 |
| #10589072 | 2 |
| #10589068 | 2 |
| #71493 | 3 |
| #69381 | 3 |