Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
310 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 6. #10588383 | C3 | direct (N × H) |
| 107. C3×C9 | #491 | semidirect |
| 150. C9 | C3×#491 | semidirect |
| 169. C3 | #10588383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63432 | 2 |
| C3×#63431 | 2 |
| C3×C9×#97 | 2 |
| C3×#63376 | 2 |
| C3×#4703 | 3 |
| #10588383 | 3 |