Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
262 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 7. C2×C9×Dic6 | C4 | semidirect |
| 12. C4×C9×Dic3 | C4 | semidirect |
| 30. #4473 | C9 | direct (N × H) |
| 96. C2×Dic6 | C4×C9 | semidirect |
| 107. C4×Dic3 | C4×C9 | semidirect |
| 138. C3×C9 | #354 | semidirect |
| 210. C9 | #4473 | direct (N × H) |
| 243. C3 | C9×#354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#936 | 2 |
| C3×C9×#99 | 2 |
| C9×#834 | 2 |
| C3×#4473 | 3 |
| C9×#354 | 3 |