Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
338 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 338 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 |
|---|---|---|
| 1. C9×#890 | C2 | semidirect |
| 4. C3×#63368 | C2 | semidirect |
| 5. #11720268 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 34. #63368 | D3 | semidirect |
| 89. #890 | D9 | semidirect |
| 200. C3×C9 | #488 | semidirect |
| 287. C9 | #4800 | semidirect |
| 325. C3 | #10588749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#890 | 2 |
| #11720952 | 2 |
| #11720528 | 2 |
| C3×#63368 | 2 |
| #11720268 | 2 |
| #11720267 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10590537 | 3 |
| #10588749 | 3 |