Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1188 conjugacy classes of subgroups.
The subgroup lattice has 279 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C32×C4×C4⋊C4 | C2 | semidirect |
| 4. C2×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 5. #10589395 | C2 | semidirect |
| 16. C4×C4⋊(C3⋊D3) | C4 | semidirect |
| 18. #63636 | C4 | direct (N × H) |
| 21. C3×C4×C4⋊C4 | D3 | semidirect |
| 39. C32×C4⋊C4 | C2×C4 | semidirect |
| 48. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 86. C4⋊(C3⋊D3) | C42 | semidirect |
| 92. C4×C4⋊C4 | C3⋊D3 | semidirect |
| 108. C3×C4⋊C4 | C4×D3 | semidirect |
| 130. C32×C4 | #102 | semidirect |
| 199. C4⋊C4 | C4×C3⋊D3 | semidirect |
| 216. C3×C4 | #809 | semidirect |
| 221. C32 | C4×#102 | semidirect |
| 267. C4 | #63636 | direct (N × H) |
| 271. C3 | C4×#809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊(C3⋊D3) | 2 |
| C32×C4×C4⋊C4 | 2 |
| C2×#63636 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| #10589395 | 2 |
| C4×#809 | 3 |