Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 227 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 |
|---|---|---|
| 90. C3×C9 | #341 | semidirect |
| 130. C9 | #4552 | semidirect |
| 150. C3 | #10588227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C8×C9 | 2 |
| C2×#88532 | 2 |
| #10589418 | 3 |
| #10588227 | 3 |