Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2065 conjugacy classes of subgroups.
The subgroup lattice has 382 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #10591220 | C2 | direct (N × H) |
| 14. C22×C3×Dic6 | C4 | semidirect |
| 45. C22×C3×Dic3 | Q8 | semidirect |
| 51. C2×C3×Dic6 | C2×C4 | semidirect |
| 71. C22×Dic6 | Dic3 | semidirect |
| 105. C2×C3×Dic3 | C2×Q8 | semidirect |
| 152. C22×Dic3 | Dic6 | semidirect |
| 159. C2×Dic6 | C2×Dic3 | semidirect |
| 246. C2×Dic3 | C2×Dic6 | semidirect |
| 249. C2×C32 | #391 | semidirect |
| 317. C32 | C2×#391 | semidirect |
| 346. C2×C3 | #4929 | semidirect |
| 347. C2×C3 | #5229 | semidirect |
| 373. C3 | C2×#4929 | semidirect |
| 374. C3 | C2×#5229 | semidirect |
| 375. C2 | #10591220 | 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 |
| #10591220 | 2 |
| C2×#5229 | 3 |
| C2×#4929 | 3 |