Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
590 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 4. #11720537 | C2 | semidirect |
| 5. C8×C3⋊Dic9 | C2 | semidirect |
| 32. C2×C3⋊Dic9 | C8 | semidirect |
| 151. C3×C9 | #431 | semidirect |
| 214. C9 | #4718 | semidirect |
| 245. C3 | #10588398 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊Dic9 | 2 |
| C3×C9×C22⋊C8 | 2 |
| #11720571 | 2 |
| #11720537 | 2 |
| C8×C3⋊Dic9 | 2 |
| #10592417 | 3 |
| #10588398 | 3 |