Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
455 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 455 conjugacy classes of subgroups — too many to draw. Only its 122 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×#5092 | C2 | semidirect |
| 3. C3×#5078 | C2 | semidirect |
| 6. C3×#4682 | C2 | semidirect |
| 7. C3×#4454 | C2 | semidirect |
| 9. #71195 | C3 | direct (N × H) |
| 31. #5092 | C2×C3 | semidirect |
| 32. #5078 | C2×C3 | semidirect |
| 35. #4682 | C2×C3 | semidirect |
| 37. #4454 | C2×C3 | semidirect |
| 269. C32 | #1722 | semidirect |
| 309. C3 | #71195 | direct (N × H) |
| 310. C3 | C3×#1722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#486 | 2 |
| C3×#5092 | 2 |
| C3×#5078 | 2 |
| C3×#5076 | 2 |
| C3×#5070 | 2 |
| C3×#4682 | 2 |
| C3×#4454 | 2 |
| C3×#1722 | 3 |
| #71195 | 3 |