Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
928 conjugacy classes of subgroups.
The subgroup lattice has 204 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. Dic3×C4⋊C4 | C2 | direct (N × H) |
| 13. C2×C3×C4⋊C4 | C4 | semidirect |
| 15. C2×C4⋊Dic3 | C4 | semidirect |
| 18. C2×C4×Dic3 | C4 | semidirect |
| 49. C3×C4⋊C4 | C2×C4 | semidirect |
| 50. C4⋊Dic3 | C2×C4 | semidirect |
| 52. C4×Dic3 | C2×C4 | semidirect |
| 60. C2×C4⋊C4 | Dic3 | direct (N × H) |
| 78. C2×C3×C4 | C42 | semidirect |
| 89. C2×Dic3 | C4⋊C4 | direct (N × H) |
| 117. C4⋊C4 | C2×Dic3 | direct (N × H) |
| 135. C3×C4 | C2×C42 | semidirect |
| 138. Dic3 | C2×C4⋊C4 | direct (N × H) |
| 162. C2×C4 | C4×Dic3 | semidirect |
| 167. C2×C3 | C4×C4⋊C4 | semidirect |
| 193. C4 | C2×C4×Dic3 | semidirect |
| 194. C3 | C2×C4×C4⋊C4 | semidirect |
| 195. C2 | Dic3×C4⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| C22×C4⋊Dic3 | 2 |
| C22×C4×Dic3 | 2 |
| C2×C3⋊#95 | 2 |
| Dic3×C4⋊C4 | 2 |
| C2×C4×C4⋊C4 | 3 |