Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
404 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 83 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. #11720913 | C2 | semidirect |
| 4. C2×#88428 | C2 | semidirect |
| 5. C9×#816 | C2 | semidirect |
| 6. C3×Dic9⋊C8 | C2 | semidirect |
| 36. Dic9⋊C8 | D3 | semidirect |
| 108. #816 | D9 | semidirect |
| 220. C3×C9 | #464 | semidirect |
| 315. C9 | #4845 | semidirect |
| 355. C3 | #10588478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| #11720953 | 2 |
| #11720913 | 2 |
| C2×#88428 | 2 |
| C9×#816 | 2 |
| C3×Dic9⋊C8 | 2 |
| #11720267 | 2 |
| #10590813 | 3 |
| #10588478 | 3 |