Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
286 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 7. C2×#6226 | C4 | semidirect |
| 10. C4×C3⋊Dic9 | C4 | semidirect |
| 147. C3×C9 | #354 | semidirect |
| 222. C9 | #4473 | semidirect |
| 255. C3 | #10588149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721836 | 2 |
| C9×#834 | 2 |
| C3×#63393 | 2 |
| #10589181 | 3 |
| #10588149 | 3 |