Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
210 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 3. C22×Dic24 | C3 | semidirect |
| 35. Dic24 | A4 | direct (N × H) |
| 63. C3×A4 | Q32 | semidirect |
| 109. C22×C3 | C3×Q32 | semidirect |
| 111. A4 | Dic24 | direct (N × H) |
| 138. C22 | C3×Dic24 | semidirect |
| 145. C3 | A4×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| A4×Dic12 | 2 |
| C3×A4×C16 | 2 |
| C22×Dic24 | 3 |
| A4×Q32 | 3 |
| C3×Dic24 | 4 |