Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
336 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 106 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×#4716 | C2 | semidirect |
| 5. C3×#4496 | C2 | semidirect |
| 6. C3×#4494 | C2 | semidirect |
| 7. C3×#4466 | C2 | semidirect |
| 9. #70928 | C3 | direct (N × H) |
| 17. C3×#829 | C4 | semidirect |
| 18. C3×#827 | C4 | semidirect |
| 29. #4716 | C2×C3 | semidirect |
| 35. #4496 | C2×C3 | semidirect |
| 36. #4494 | C2×C3 | semidirect |
| 37. #4466 | C2×C3 | semidirect |
| 82. #829 | C3×C4 | semidirect |
| 83. #827 | C3×C4 | semidirect |
| 257. C32 | #2180 | semidirect |
| 290. C3 | #70928 | direct (N × H) |
| 291. C3 | C3×#2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#444 | 2 |
| C3×#5195 | 2 |
| C3×#4716 | 2 |
| C3×#4566 | 2 |
| C3×#4496 | 2 |
| C3×#4494 | 2 |
| C3×#4466 | 2 |
| C3×#2180 | 3 |
| #70928 | 3 |