Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
217 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 217 conjugacy classes of subgroups — too many to draw. Only its 29 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 |
|---|---|---|
| 1. C9⋊(#95⋊C3) | C2 | semidirect |
| 3. C9×#392 | C3 | semidirect |
| 4. #392⋊C9 | C3 | semidirect |
| 40. #392 | 3−1+2 | semidirect |
| 104. C9 | #392⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9⋊(#95⋊C3) | 2 |
| C3×#392⋊C3 | 3 |
| C9×#392 | 3 |
| #392⋊C9 | 3 |
| C4×C9⋊A4 | 4 |