Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
338 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 1. C32×#441 | C2 | semidirect |
| 4. C3×#4565 | C2 | semidirect |
| 6. C3×#4487 | C2 | semidirect |
| 7. C3×#4466 | C2 | semidirect |
| 9. #70917 | C3 | direct (N × H) |
| 17. C3×#829 | C4 | semidirect |
| 18. C3×#828 | C4 | semidirect |
| 26. C3×#441 | D3 | semidirect |
| 27. C3×#441 | C2×C3 | semidirect |
| 34. #4565 | C2×C3 | semidirect |
| 36. #4487 | C2×C3 | semidirect |
| 37. #4466 | C2×C3 | semidirect |
| 82. #829 | C3×C4 | semidirect |
| 83. #828 | C3×C4 | semidirect |
| 104. #441 | C3×D3 | semidirect |
| 255. C32 | #2180 | semidirect |
| 287. C3 | #70917 | direct (N × H) |
| 288. C3 | C3×#2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#441 | 2 |
| C3×#5179 | 2 |
| C3×#4717 | 2 |
| C3×#4565 | 2 |
| C3×#4488 | 2 |
| C3×#4487 | 2 |
| C3×#4466 | 2 |
| C3×#2180 | 3 |
| #70917 | 3 |