Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. C2×#88521 | C2 | semidirect |
| 3. #11720964 | C2 | semidirect |
| 4. C2×#88424 | C2 | semidirect |
| 5. C3×C8×Dic9 | C2 | semidirect |
| 27. C8×Dic9 | D3 | semidirect |
| 152. C3×C9 | #495 | semidirect |
| 215. C9 | #4696 | semidirect |
| 242. C3 | #10588835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| C2×C9×D24 | 2 |
| #11720964 | 2 |
| C2×#88424 | 2 |
| C3×C8×Dic9 | 2 |
| #10590864 | 3 |
| #10588835 | 3 |