Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
269 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 269 conjugacy classes of subgroups — too many to draw. Only its 90 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. C3×#4858 | C2 | semidirect |
| 5. C3×#4513 | C2 | semidirect |
| 6. C3×#4511 | C2 | semidirect |
| 7. C3×#4487 | C2 | semidirect |
| 9. #69247 | C3 | direct (N × H) |
| 24. #4858 | C2×C3 | semidirect |
| 33. #4513 | C2×C3 | semidirect |
| 34. #4511 | C2×C3 | semidirect |
| 35. #4487 | C2×C3 | semidirect |
| 231. C32 | #2231 | semidirect |
| 263. C3 | #69247 | direct (N × H) |
| 264. C3 | C3×#2231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5196 | 2 |
| C3×#4858 | 2 |
| C32×#360 | 2 |
| C3×#4566 | 2 |
| C3×#4513 | 2 |
| C3×#4511 | 2 |
| C3×#4487 | 2 |
| C3×#2231 | 3 |
| #69247 | 3 |