Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
199 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 35 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⋊(C22⋊SL(2,𝔽3)) | C2 | semidirect |
| 3. C9×#393 | C3 | semidirect |
| 4. #393⋊C9 | C3 | semidirect |
| 7. C22×Q8×C9 | C2×C3 | semidirect |
| 8. C22⋊(Q8⋊C9) | C2×C3 | semidirect |
| 34. C23×C9 | SL(2,𝔽3) | semidirect |
| 45. #393 | 3−1+2 | semidirect |
| 66. C22×Q8 | C2×3−1+2 | semidirect |
| 108. C9 | #393⋊C3 | semidirect |
| 111. C23 | C9⋊SL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9⋊(C22⋊SL(2,𝔽3)) | 2 |
| C3×#393⋊C3 | 3 |
| C9×#393 | 3 |
| #393⋊C9 | 3 |
| C22×C9⋊A4 | 4 |