Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. C9×#887 | C2 | semidirect |
| 3. C2×#88427 | C2 | semidirect |
| 6. C3×#63368 | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 36. #63368 | D3 | semidirect |
| 101. #887 | D9 | semidirect |
| 216. C3×C9 | #464 | semidirect |
| 309. C9 | #4798 | semidirect |
| 349. C3 | #10588711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#887 | 2 |
| #11720952 | 2 |
| C2×#88427 | 2 |
| C2×#88426 | 2 |
| #11720528 | 2 |
| C3×#63368 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10590536 | 3 |
| #10588711 | 3 |