Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2105 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #10591221 | C2 | direct (N × H) |
| 14. C22×C3×Dic6 | C4 | semidirect |
| 39. C22×C3⋊Dic3 | Q8 | semidirect |
| 51. C2×C3×Dic6 | C2×C4 | semidirect |
| 71. C22×Dic6 | Dic3 | semidirect |
| 98. C2×C3⋊Dic3 | C2×Q8 | semidirect |
| 160. C2×Dic6 | C2×Dic3 | semidirect |
| 251. C2×C32 | #391 | semidirect |
| 319. C32 | C2×#391 | semidirect |
| 348. C2×C3 | #4973 | semidirect |
| 349. C2×C3 | #5229 | semidirect |
| 375. C3 | C2×#4973 | semidirect |
| 376. C3 | C2×#5229 | semidirect |
| 377. C2 | #10591221 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×Dic6 | 2 |
| C22×C4×C3⋊Dic3 | 2 |
| C22×C3×C4⋊Dic3 | 2 |
| C2×#63579 | 2 |
| #10591221 | 2 |
| C2×#5229 | 3 |
| C2×#4973 | 3 |