Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
222 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 222 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 |
|---|---|---|
| 27. #4565 | C9 | direct (N × H) |
| 109. C3×C9 | #362 | semidirect |
| 156. C9 | #4565 | direct (N × H) |
| 175. C3 | C9×#362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| C9×#819 | 2 |
| C9×#812 | 2 |
| C3×#4565 | 3 |
| C9×#362 | 3 |