Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
358 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 92 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. 3−1+2×#125 | C2 | semidirect |
| 3. #63369⋊C3 | C2 | semidirect |
| 4. #63362⋊C3 | C2 | semidirect |
| 6. #10588748 | C3 | semidirect |
| 18. C9×#125 | C2×C3 | semidirect |
| 20. #63369 | C2×C3 | semidirect |
| 21. #63362 | C2×C3 | semidirect |
| 110. #125 | AGL(1,ℤ/9) | semidirect |
| 113. 3−1+2 | #490 | semidirect |
| 156. C9 | C3×#490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#125 | 2 |
| #11721394 | 2 |
| #63369⋊C3 | 2 |
| #63362⋊C3 | 2 |
| C3×#5067 | 3 |
| #10588748 | 3 |