Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
286 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. C9×#803 | C2 | semidirect |
| 23. #4540 | C9 | direct (N × H) |
| 48. #803 | C2×C9 | semidirect |
| 107. C3×C9 | #329 | semidirect |
| 162. C9 | #4540 | direct (N × H) |
| 186. C3 | C9×#329 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#124 | 2 |
| C9×#803 | 2 |
| C3×#4540 | 3 |
| C9×#329 | 3 |