Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1536 conjugacy classes of subgroups.
The subgroup lattice has 216 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10589417 | C2 | direct (N × H) |
| 8. C22×C32×C8 | C4 | semidirect |
| 12. C2×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 30. C2×C32×C8 | C2×C4 | semidirect |
| 33. C4⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 38. C22×C3×C8 | Dic3 | semidirect |
| 80. C2×C3×C8 | C2×Dic3 | semidirect |
| 102. C22×C8 | C3⋊Dic3 | semidirect |
| 128. C2×C32 | #340 | semidirect |
| 147. C2×C8 | C2×C3⋊Dic3 | semidirect |
| 166. C32 | C2×#340 | semidirect |
| 187. C2×C3 | #4551 | semidirect |
| 208. C3 | C2×#4551 | semidirect |
| 209. C2 | #10589417 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C32×C8 | 2 |
| C22×C4⋊(C3⋊Dic3) | 2 |
| #10589417 | 2 |
| C2×#4551 | 3 |