Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
360 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 124 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 |
|---|---|---|
| 3. 3−1+2×#107 | C2 | semidirect |
| 4. #63378⋊C3 | C2 | semidirect |
| 5. #63367⋊C3 | C2 | semidirect |
| 7. #10588560 | C3 | semidirect |
| 15. C8×AGL(1,ℤ/9) | C4 | semidirect |
| 24. C9×#107 | C2×C3 | semidirect |
| 25. #63378 | C2×C3 | semidirect |
| 26. #63367 | C2×C3 | semidirect |
| 55. C8×D9 | C3×C4 | semidirect |
| 142. #107 | AGL(1,ℤ/9) | semidirect |
| 144. 3−1+2 | #427 | semidirect |
| 202. C9 | C3×#427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×AGL(1,ℤ/9) | 2 |
| #63454⋊C3 | 2 |
| 3−1+2×#107 | 2 |
| #63378⋊C3 | 2 |
| #63367⋊C3 | 2 |
| C3×#4880 | 3 |
| #10588560 | 3 |