Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 8. C2×C9×Dic6 | C4 | semidirect |
| 10. C9×C4⋊Dic3 | C4 | semidirect |
| 32. #4452 | C9 | direct (N × H) |
| 108. C2×Dic6 | C4×C9 | semidirect |
| 114. C4⋊Dic3 | C4×C9 | semidirect |
| 148. C3×C9 | #328 | semidirect |
| 230. C9 | #4452 | direct (N × H) |
| 268. C3 | C9×#328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#924 | 2 |
| C3×C9×#95 | 2 |
| C9×#830 | 2 |
| C3×#4452 | 3 |
| C9×#328 | 3 |