Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
291 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 81 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. C9×2−1+4⋊C3 | C2 | semidirect |
| 2. C9×#994 | C2 | semidirect |
| 3. C9×#131⋊C3 | C2 | semidirect |
| 5. C9×#577 | C3 | semidirect |
| 6. #577⋊C9 | C3 | semidirect |
| 15. C9×H(5,𝔽2) | C2×C3 | semidirect |
| 17. #63700 | C2×C3 | semidirect |
| 22. C9×#131 | C2×C3 | semidirect |
| 23. #131⋊C9 | C2×C3 | semidirect |
| 29. #577⋊C3 | C9 | direct (N × H) |
| 59. 2−1+4⋊C3 | C2×C9 | semidirect |
| 60. #994 | C2×C9 | semidirect |
| 66. #131⋊C3 | C2×C9 | semidirect |
| 92. #577 | C3×C9 | semidirect |
| 130. H(5,𝔽2) | C2×C3×C9 | semidirect |
| 135. #131 | C2×C3×C9 | semidirect |
| 195. C9 | #577⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×2−1+4⋊C3 | 2 |
| C9×#994 | 2 |
| C9×#131⋊C3 | 2 |
| C3×#577⋊C3 | 3 |
| C9×#577 | 3 |
| #577⋊C9 | 3 |
| C3×C9×SD16 | 4 |