Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
358 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 113 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. C4×C9×SL(2,𝔽3) | C2 | semidirect |
| 4. C9×#519 | C3 | semidirect |
| 5. #519⋊C9 | C3 | semidirect |
| 6. C2×C9×SL(2,𝔽3) | C4 | semidirect |
| 14. C4×Q8×C9 | C2×C3 | semidirect |
| 17. C4×Q8⋊C9 | C2×C3 | semidirect |
| 22. #519⋊C3 | C9 | direct (N × H) |
| 28. C2×Q8×C9 | C3×C4 | semidirect |
| 31. C2×Q8⋊C9 | C3×C4 | semidirect |
| 50. C4×SL(2,𝔽3) | C2×C9 | semidirect |
| 68. #519 | C3×C9 | semidirect |
| 77. C2×SL(2,𝔽3) | C4×C9 | semidirect |
| 104. C4×Q8 | C2×C3×C9 | semidirect |
| 133. C2×Q8 | C3×C4×C9 | semidirect |
| 156. C9 | #519⋊C3 | 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 |
| C4×C9×SL(2,𝔽3) | 2 |
| C3×#519⋊C3 | 3 |
| C9×#519 | 3 |
| #519⋊C9 | 3 |
| C3×C9×C22⋊C4 | 4 |