Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
720 conjugacy classes of subgroups.
The subgroup lattice has 306 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 37. C32×C4⋊C4 | C8 | semidirect |
| 114. C3×C4⋊C4 | C3⋊C8 | semidirect |
| 219. C4⋊C4 | C3⋊(C3⋊C8) | semidirect |
| 243. C32 | #1916 | semidirect |
| 297. C3 | #69482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×C4⋊C4 | 2 |
| C2×C4⋊(C3⋊(C3⋊C8)) | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #10589390 | 2 |
| #69482 | 3 |