Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
223 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 19. C4⋊#226 | C9 | direct (N × H) |
| 86. C4×C9 | #226 | semidirect |
| 138. C9 | C4⋊#226 | direct (N × H) |
| 162. C4 | C9×#226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#226 | 2 |
| C4×C9×SL(2,𝔽3) | 2 |
| C3×C4⋊#226 | 3 |
| C9×#462 | 3 |
| C9×C4⋊Dic3 | 4 |