Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
610 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 234 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 |
|---|---|---|
| 5. #10588328 | C3 | direct (N × H) |
| 9. C3×C4×Dic9 | C4 | semidirect |
| 34. C4×Dic9 | C3×C4 | semidirect |
| 97. C3×C9 | #376 | semidirect |
| 146. C9 | C3×#376 | semidirect |
| 170. C3 | #10588328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×Dic9 | 2 |
| C3×C9×#95 | 2 |
| C3×C9⋊#95 | 2 |
| C3×#4648 | 3 |
| #10588328 | 3 |