Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
314 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 33. #5065 | C9 | direct (N × H) |
| 125. C3×C9 | #499 | semidirect |
| 173. C9 | #5065 | direct (N × H) |
| 193. C3 | C9×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#125 | 2 |
| C9×#870 | 2 |
| C9×#808 | 2 |
| C9×#807 | 2 |
| C4×C9×C3⋊C8 | 2 |
| C3×#5065 | 3 |
| C9×#499 | 3 |