Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
234 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 9. #88521 | C4 | semidirect |
| 113. C3×C9 | #358 | semidirect |
| 165. C9 | #4503 | semidirect |
| 188. C3 | #10588169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| C9×#818 | 2 |
| C2×C3×C9⋊C16 | 2 |
| #10589119 | 3 |
| #10588169 | 3 |