Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. C9×Dic3⋊C8 | C2 | semidirect |
| 5. C3×Dic9⋊C8 | C2 | semidirect |
| 6. Dic9⋊(C3⋊C8) | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 36. Dic9⋊C8 | D3 | semidirect |
| 106. Dic3⋊C8 | D9 | semidirect |
| 213. C3×C9 | #424 | semidirect |
| 303. C9 | #4839 | semidirect |
| 341. C3 | #10588523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88523 | 2 |
| #11720931 | 2 |
| C2×(C3⋊D9)⋊C8 | 2 |
| C9×Dic3⋊C8 | 2 |
| C3×Dic9⋊C8 | 2 |
| Dic9⋊(C3⋊C8) | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10590702 | 3 |
| #10588523 | 3 |