Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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×#63432 | C2 | semidirect |
| 3. C4×C3⋊(C9⋊C8) | C2 | semidirect |
| 4. #11720297 | C2 | semidirect |
| 21. #63432 | D3 | semidirect |
| 131. C3×C9 | #488 | semidirect |
| 185. C9 | #5068 | semidirect |
| 210. C3 | #10588735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#875 | 2 |
| C3×#63432 | 2 |
| C4×C3⋊(C9⋊C8) | 2 |
| #11720297 | 2 |
| #11720294 | 2 |
| #10590278 | 3 |
| #10588735 | 3 |