Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
233 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 233 conjugacy classes of subgroups — too many to draw. Only its 75 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. C9×#557 | C3 | semidirect |
| 5. #557⋊C9 | C3 | semidirect |
| 19. C9⋊SL(2,𝔽3) | Q8 | semidirect |
| 59. #557 | 3−1+2 | semidirect |
| 134. C9 | #557⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9⋊SL(2,𝔽3) | 2 |
| C3×#557⋊C3 | 3 |
| C9×#557 | 3 |
| #557⋊C9 | 3 |
| C4⋊C4×3−1+2 | 4 |