Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
285 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 2. C9×#859 | C2 | semidirect |
| 5. C2×C9×SL(2,𝔽3) | C4 | semidirect |
| 19. #5420 | C9 | direct (N × H) |
| 26. C2×Q8×C9 | Dic3 | semidirect |
| 45. #859 | C2×C9 | semidirect |
| 75. C2×SL(2,𝔽3) | C4×C9 | semidirect |
| 130. C2×Q8 | C9×Dic3 | semidirect |
| 154. C9 | #5420 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×SL(2,𝔽3) | 2 |
| C9×#859 | 2 |
| C3×#5420 | 3 |
| C9×#419 | 3 |
| C9×#217 | 4 |