Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
890 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 890 conjugacy classes of subgroups — too many to draw. Only its 299 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 |
|---|---|---|
| 9. C4×C3⋊Dic9 | C4 | semidirect |
| 86. C3×C9 | #376 | semidirect |
| 124. C9 | #4648 | semidirect |
| 144. C3 | #10588328 | 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×#95 | 2 |
| #11720572 | 2 |
| #10592347 | 3 |
| #10588328 | 3 |