Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
353 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 353 conjugacy classes of subgroups — too many to draw. Only its 80 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. #10590918 | C2 | semidirect |
| 3. #10590768 | C2 | semidirect |
| 4. C3×#4513 | C2 | semidirect |
| 5. C3×#4512 | C2 | semidirect |
| 6. #10589128 | C2 | semidirect |
| 7. #10589125 | C2 | semidirect |
| 15. #63627 | C4 | semidirect |
| 16. #63626 | C4 | semidirect |
| 34. #4513 | D3 | semidirect |
| 35. #4512 | D3 | semidirect |
| 42. #3746 | C2×C4 | semidirect |
| 45. #3745 | C2×C4 | semidirect |
| 54. C32×C16 | C2×C4 | semidirect |
| 152. C3×C16 | C4×D3 | semidirect |
| 153. C3×C16 | C4×D3 | semidirect |
| 239. C16 | #624 | semidirect |
| 268. C32 | AGL(1,ℤ/16) | semidirect |
| 307. C3 | #69091 | semidirect |
| 308. C3 | #69310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592607 | 2 |
| #10590918 | 2 |
| #10590768 | 2 |
| C3×#4513 | 2 |
| C3×#4512 | 2 |
| #10589128 | 2 |
| #10589125 | 2 |
| #69310 | 3 |
| #69091 | 3 |