Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
269 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 269 conjugacy classes of subgroups — too many to draw. Only its 82 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. C32×#365 | C2 | semidirect |
| 4. C3×#4517 | C2 | semidirect |
| 6. C3×#4496 | C2 | semidirect |
| 7. C3×#4487 | C2 | semidirect |
| 9. #69314 | C3 | direct (N × H) |
| 27. C3×#365 | D3 | semidirect |
| 28. C3×#365 | C2×C3 | semidirect |
| 32. #4517 | C2×C3 | semidirect |
| 34. #4496 | C2×C3 | semidirect |
| 35. #4487 | C2×C3 | semidirect |
| 96. #365 | C3×D3 | semidirect |
| 230. C32 | #2239 | semidirect |
| 262. C3 | #69314 | direct (N × H) |
| 263. C3 | C3×#2239 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4893 | 2 |
| C3×#4867 | 2 |
| C32×#365 | 2 |
| C3×#4517 | 2 |
| C3×#4514 | 2 |
| C3×#4496 | 2 |
| C3×#4487 | 2 |
| C3×#2239 | 3 |
| #69314 | 3 |