Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
384 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 92. C9×Dic3 | Q16 | semidirect |
| 211. C3×C9 | #462 | semidirect |
| 294. Dic3 | #3674 | semidirect |
| 297. C9 | #5182 | semidirect |
| 332. C3 | #10588707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88547 | 2 |
| Q8×C9×Dic3 | 2 |
| C2×C3×#3674 | 2 |
| #11720932 | 2 |
| #11720269 | 2 |
| #11720268 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10591625 | 3 |
| #10588707 | 3 |