Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
250 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×A4×C16 | C2 | semidirect |
| 3. A4×C3⋊C16 | C2 | semidirect |
| 4. C22×D3×C16 | C3 | semidirect |
| 12. C22×C3×C16 | C2×C3 | semidirect |
| 13. C22×C3⋊C16 | C2×C3 | semidirect |
| 20. A4×C16 | D3 | direct (N × H) |
| 48. D3×C16 | A4 | direct (N × H) |
| 50. D3×A4 | C16 | direct (N × H) |
| 60. C22×C16 | C3×D3 | semidirect |
| 86. C3×C16 | C2×A4 | semidirect |
| 88. C3⋊C16 | C2×A4 | semidirect |
| 90. C3×A4 | C2×C16 | semidirect |
| 113. C22×D3 | C3×C16 | semidirect |
| 155. C16 | D3×A4 | direct (N × H) |
| 159. C22×C3 | C2×C3×C16 | semidirect |
| 167. A4 | D3×C16 | direct (N × H) |
| 201. D3 | A4×C16 | direct (N × H) |
| 210. C22 | C3×D3×C16 | semidirect |
| 217. C3 | C2×A4×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C8×A4 | 2 |
| C3×A4×C16 | 2 |
| A4×C3⋊C16 | 2 |
| C22×D3×C16 | 3 |
| C2×A4×C16 | 3 |
| C3×D3×C16 | 4 |