Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
367 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 367 conjugacy classes of subgroups — too many to draw. Only its 88 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×#4694 | C2 | semidirect |
| 2. C3×#4688 | C2 | semidirect |
| 4. #10590266 | C2 | semidirect |
| 5. #10589324 | C2 | semidirect |
| 6. #10589095 | C2 | semidirect |
| 7. #10589090 | C2 | semidirect |
| 31. #4694 | D3 | semidirect |
| 32. #4688 | D3 | semidirect |
| 299. C32 | #1697 | semidirect |
| 350. C3 | #70869 | semidirect |
| 351. C3 | #71202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4694 | 2 |
| C3×#4688 | 2 |
| #10590347 | 2 |
| #10590266 | 2 |
| #10589324 | 2 |
| #10589095 | 2 |
| #10589090 | 2 |
| #71202 | 3 |
| #70869 | 3 |