Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
329 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 329 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 |
|---|---|---|
| 2. #10590916 | C2 | semidirect |
| 3. #10590771 | C2 | semidirect |
| 4. #10589379 | C2 | semidirect |
| 5. C3×#4512 | C2 | semidirect |
| 6. #10589127 | C2 | semidirect |
| 7. #10589124 | C2 | semidirect |
| 19. C3×#800 | C4 | semidirect |
| 20. C3×D48 | C4 | semidirect |
| 37. #4512 | D3 | semidirect |
| 46. C3×Dic12 | C2×C4 | semidirect |
| 49. C3×D24 | C2×C4 | semidirect |
| 54. C32×C16 | C2×C4 | semidirect |
| 84. #800 | Dic3 | semidirect |
| 85. D48 | Dic3 | semidirect |
| 136. Dic12 | C2×Dic3 | semidirect |
| 139. D24 | C2×Dic3 | semidirect |
| 145. C3×C16 | C4×D3 | semidirect |
| 146. C3×C16 | C2×Dic3 | semidirect |
| 227. C16 | D3×Dic3 | semidirect |
| 252. C32 | AGL(1,ℤ/16) | semidirect |
| 289. C3 | #69091 | semidirect |
| 290. C3 | #71515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4908 | 2 |
| #10590916 | 2 |
| #10590771 | 2 |
| #10589379 | 2 |
| C3×#4512 | 2 |
| #10589127 | 2 |
| #10589124 | 2 |
| #71515 | 3 |
| #69091 | 3 |