Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 450 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. C2×#88547 | C2 | semidirect |
| 2. C9×#947 | C2 | semidirect |
| 3. C2×C3×#3675 | C2 | semidirect |
| 4. #11720948 | C2 | semidirect |
| 5. C2×#88424 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 31. C2×#3675 | D3 | semidirect |
| 98. #947 | D9 | semidirect |
| 218. C3×C9 | #495 | semidirect |
| 309. C9 | #5168 | semidirect |
| 347. C3 | #10588740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88547 | 2 |
| C9×#947 | 2 |
| C2×C3×#3675 | 2 |
| #11720948 | 2 |
| C2×#88424 | 2 |
| C2×#88421 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10591606 | 3 |
| #10588740 | 3 |