Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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. #11720509 | C2 | semidirect |
| 3. C9×Dic24 | C2 | semidirect |
| 5. #11720245 | C2 | semidirect |
| 65. Dic24 | D9 | direct (N × H) |
| 85. C3×D9 | Q32 | semidirect |
| 119. C3×C9 | C2×Q32 | semidirect |
| 140. D9 | Dic24 | direct (N × H) |
| 162. C9 | C2×Dic24 | semidirect |
| 181. C3 | D9×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D9×Dic12 | 2 |
| #11720509 | 2 |
| C9×Dic24 | 2 |
| C3×C16×D9 | 2 |
| #11720245 | 2 |
| D3×Dic24 | 3 |
| D9×Q32 | 3 |