Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
466 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 466 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×#63498 | C2 | semidirect |
| 3. C2×C9×#214 | C2 | semidirect |
| 4. #11720953 | C2 | semidirect |
| 5. C2×#88427 | C2 | semidirect |
| 6. C2×#88416 | C2 | semidirect |
| 7. C3⋊C8×Dic9 | C2 | semidirect |
| 33. #63498 | D3 | semidirect |
| 103. C2×#214 | D9 | semidirect |
| 220. C3×C9 | #495 | semidirect |
| 315. C9 | #5059 | semidirect |
| 355. C3 | #10588848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88544 | 2 |
| C3×#63498 | 2 |
| C2×C9×#214 | 2 |
| #11720953 | 2 |
| C2×#88427 | 2 |
| C2×#88416 | 2 |
| C3⋊C8×Dic9 | 2 |
| #10591473 | 3 |
| #10588848 | 3 |