Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1233 conjugacy classes of subgroups.
The subgroup lattice has 505 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #10589164 | C2 | direct (N × H) |
| 12. C2×C4⋊(C3⋊Dic3) | C4 | semidirect |
| 16. C2×C3×C4⋊Dic3 | C4 | semidirect |
| 20. C22×C3×C3⋊C8 | C4 | semidirect |
| 50. C4⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 53. C3×C4⋊Dic3 | C2×C4 | semidirect |
| 57. C2×C3×C3⋊C8 | C2×C4 | semidirect |
| 89. C2×C4⋊Dic3 | Dic3 | semidirect |
| 93. C22×C3⋊C8 | Dic3 | semidirect |
| 194. C4⋊Dic3 | C2×Dic3 | semidirect |
| 198. C2×C3⋊C8 | C2×Dic3 | semidirect |
| 320. C2×C32 | #340 | semidirect |
| 417. C32 | C2×#340 | semidirect |
| 456. C2×C3 | #4529 | semidirect |
| 457. C2×C3 | #4551 | semidirect |
| 494. C3 | C2×#4529 | semidirect |
| 495. C3 | C2×#4551 | semidirect |
| 496. C2 | #10589164 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊Dic3) | 2 |
| C22×C3×C4⋊Dic3 | 2 |
| C23×C3×C3⋊C8 | 2 |
| #10589164 | 2 |
| C2×#4551 | 3 |
| C2×#4529 | 3 |