Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
393 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 3. C3×#4682 | C2 | semidirect |
| 4. C3×#4486 | C2 | semidirect |
| 5. C3×#4457 | C2 | semidirect |
| 7. #70873 | C3 | direct (N × H) |
| 25. #4682 | C2×C3 | semidirect |
| 28. #4486 | C2×C3 | semidirect |
| 29. #4457 | C2×C3 | semidirect |
| 85. C32×C8 | SD16 | semidirect |
| 188. C3×C8 | #214 | semidirect |
| 189. C3×C8 | C3×SD16 | semidirect |
| 238. C32 | #1693 | semidirect |
| 253. C8 | C3×#214 | semidirect |
| 277. C3 | #70873 | direct (N × H) |
| 278. C3 | C3×#1693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#436 | 2 |
| C3×#5019 | 2 |
| C3×#4682 | 2 |
| C3×#4486 | 2 |
| C3×#4457 | 2 |
| C3×#1693 | 3 |
| #70873 | 3 |