Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
284 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 28. C2×C9×Dic3 | C8 | semidirect |
| 142. C3×C9 | #324 | semidirect |
| 164. C2×Dic3 | C9⋊C8 | semidirect |
| 219. C9 | #4469 | semidirect |
| 256. C3 | #10588205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×Dic3⋊C4 | 2 |
| #11720571 | 2 |
| C3×#63389 | 2 |
| #10589147 | 3 |
| #10588205 | 3 |