Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
604 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 234 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. C32×Dic24 | C2 | direct (N × H) |
| 5. C2×C3×Dic24 | C3 | direct (N × H) |
| 17. C3×Dic24 | C2×C3 | direct (N × H) |
| 25. C2×Dic24 | C32 | direct (N × H) |
| 48. Dic24 | C2×C32 | direct (N × H) |
| 65. C2×C33 | Q32 | semidirect |
| 93. C33 | C2×Q32 | semidirect |
| 111. C2×C32 | Dic24 | direct (N × H) |
| 112. C2×C32 | C3×Q32 | semidirect |
| 132. C32 | C2×Dic24 | direct (N × H) |
| 133. C32 | C2×C3×Q32 | semidirect |
| 142. C2×C3 | C3×Dic24 | direct (N × H) |
| 143. C2×C3 | C32×Q32 | semidirect |
| 151. C3 | C2×C3×Dic24 | direct (N × H) |
| 152. C3 | C2×C32×Q32 | semidirect |
| 153. C2 | C32×Dic24 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Dic12 | 2 |
| C2×C33×C16 | 2 |
| C32×Dic24 | 2 |
| C2×C32×Q32 | 3 |
| C2×C3×Dic24 | 3 |