Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
199 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 22. C9×SL(2,𝔽3) | Q8 | semidirect |
| 118. SL(2,𝔽3) | Dic18 | semidirect |
| 154. C9 | #5391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| SL(2,𝔽3)×Dic9 | 2 |
| C9⋊#859 | 2 |
| C9×#859 | 2 |
| #10593202 | 3 |
| #10588473 | 3 |
| Dic9⋊Dic3 | 4 |