Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1116 conjugacy classes of subgroups.
The subgroup lattice has 327 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10592634 | C2 | semidirect |
| 4. C2×C4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 5. #10589395 | C2 | semidirect |
| 10. C32×C4×D4 | C4 | semidirect |
| 56. C3×C4×D4 | Dic3 | semidirect |
| 77. C32×D4 | C4⋊C4 | semidirect |
| 146. C32×C4 | #102 | semidirect |
| 156. C4×D4 | C3⋊Dic3 | semidirect |
| 176. C3×D4 | C4⋊Dic3 | semidirect |
| 248. C3×C4 | #832 | semidirect |
| 254. C32 | #1802 | semidirect |
| 266. D4 | C4⋊(C3⋊Dic3) | semidirect |
| 312. C4 | #63659 | semidirect |
| 317. C3 | #71604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×D4 | 2 |
| C2×#63659 | 2 |
| #10592634 | 2 |
| C2×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589395 | 2 |
| #71604 | 3 |