Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 96 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×#124 | C2 | semidirect |
| 2. C2×#3675⋊C3 | C2 | semidirect |
| 4. C4×C4⋊AGL(1,ℤ/9) | C2 | semidirect |
| 5. #63395⋊C3 | C2 | semidirect |
| 6. #63392⋊C3 | C2 | semidirect |
| 7. C4⋊(3−1+2⋊C8) | C2 | semidirect |
| 9. #10588738 | C3 | semidirect |
| 31. C9×#124 | C2×C3 | semidirect |
| 32. C2×#3675 | C2×C3 | semidirect |
| 34. C4×D36 | C2×C3 | semidirect |
| 35. #63395 | C2×C3 | semidirect |
| 36. #63392 | C2×C3 | semidirect |
| 37. C4⋊(C9⋊C8) | C2×C3 | semidirect |
| 224. #124 | AGL(1,ℤ/9) | semidirect |
| 229. 3−1+2 | #463 | semidirect |
| 317. C9 | C3×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| 3−1+2×#124 | 2 |
| C2×#3675⋊C3 | 2 |
| C2×#3673⋊C3 | 2 |
| C4×C4⋊AGL(1,ℤ/9) | 2 |
| #63395⋊C3 | 2 |
| #63392⋊C3 | 2 |
| C4⋊(3−1+2⋊C8) | 2 |
| C3×#5057 | 3 |
| #10588738 | 3 |