Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1488 conjugacy classes of subgroups.
The subgroup lattice has 291 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 22. #64078 | C4 | semidirect |
| 47. C32×C4⋊C4 | Q8 | semidirect |
| 53. C4⋊(C3⋊Dic3) | Q8 | semidirect |
| 121. C3×C4⋊C4 | Dic6 | semidirect |
| 213. C4⋊C4 | #634 | semidirect |
| 233. C32 | #2369 | semidirect |
| 282. C3 | #73656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64078 | 2 |
| C32×C4×C4⋊C4 | 2 |
| C4⋊C4×C3⋊Dic3 | 2 |
| #10592671 | 2 |
| C4×C4⋊(C3⋊Dic3) | 2 |
| #10592627 | 2 |
| #10592345 | 2 |
| #73656 | 3 |