Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
313 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 313 conjugacy classes of subgroups — too many to draw. Only its 102 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×#4853 | C2 | semidirect |
| 5. C3×#4517 | C2 | semidirect |
| 6. C3×#4512 | C2 | semidirect |
| 7. C3×#4487 | C2 | semidirect |
| 9. #69248 | C3 | direct (N × H) |
| 17. C3×#829 | C4 | semidirect |
| 18. C3×#827 | C4 | semidirect |
| 28. #4853 | C2×C3 | semidirect |
| 35. #4517 | C2×C3 | semidirect |
| 36. #4512 | C2×C3 | semidirect |
| 37. #4487 | C2×C3 | semidirect |
| 80. #829 | C3×C4 | semidirect |
| 81. #827 | C3×C4 | semidirect |
| 250. C32 | #2180 | semidirect |
| 283. C3 | #69248 | direct (N × H) |
| 284. C3 | C3×#2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5197 | 2 |
| C3×#5195 | 2 |
| C3×#4853 | 2 |
| C32×#360 | 2 |
| C3×#4517 | 2 |
| C3×#4512 | 2 |
| C3×#4487 | 2 |
| C3×#2180 | 3 |
| #69248 | 3 |