Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
275 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×C9×#41⋊C3 | C2 | semidirect |
| 2. C2×C9×GL(2,𝔽3) | C2 | semidirect |
| 3. C9×#859 | C2 | semidirect |
| 13. C2×C9×#41 | D3 | semidirect |
| 24. C9×SL(2,𝔽3) | D4 | semidirect |
| 25. #5427 | C9 | direct (N × H) |
| 55. C2×#41⋊C3 | C2×C9 | semidirect |
| 56. C2×GL(2,𝔽3) | C2×C9 | semidirect |
| 60. #859 | C2×C9 | semidirect |
| 130. C2×#41 | D3×C9 | semidirect |
| 157. SL(2,𝔽3) | D4×C9 | semidirect |
| 207. C9 | #5427 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#41⋊C3 | 2 |
| C2×C9×GL(2,𝔽3) | 2 |
| C9×#859 | 2 |
| C3×#5427 | 3 |
| C9×#449 | 3 |
| C9×(C2×D3)⋊C4 | 4 |