Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
302 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 27. #4683 | C9 | direct (N × H) |
| 103. C3×C9 | #499 | semidirect |
| 145. C9 | #4683 | direct (N × H) |
| 163. C3 | C9×#499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#870 | 2 |
| C3×C4×C8×C9 | 2 |
| C9×#818 | 2 |
| C9×#817 | 2 |
| C3×#4683 | 3 |
| C9×#499 | 3 |