Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
832 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 832 conjugacy classes of subgroups — too many to draw. Only its 150 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. C3×#64141 | C2 | semidirect |
| 2. C2×C3×#3753 | C2 | semidirect |
| 3. C3×#64117 | C2 | semidirect |
| 4. C3×#64116 | C2 | semidirect |
| 5. C33×#100 | C2 | semidirect |
| 6. C3×#63650 | C2 | semidirect |
| 7. C3×#63649 | C2 | semidirect |
| 8. #10592448 | C3 | direct (N × H) |
| 25. #64141 | C2×C3 | semidirect |
| 26. C2×#3753 | C2×C3 | semidirect |
| 27. #64117 | C2×C3 | semidirect |
| 28. #64116 | C2×C3 | semidirect |
| 34. C32×#100 | D3 | semidirect |
| 35. C32×#100 | C2×C3 | semidirect |
| 36. #63650 | C2×C3 | semidirect |
| 37. #63649 | C2×C3 | semidirect |
| 111. C3×#100 | C3×D3 | semidirect |
| 112. C3×#100 | C3⋊D3 | semidirect |
| 221. #100 | C3×C3⋊D3 | semidirect |
| 222. C33 | #472 | semidirect |
| 313. C32 | #4749 | semidirect |
| 314. C32 | C3×#472 | semidirect |
| 354. C3 | C3×#4749 | semidirect |
| 355. C3 | #10592448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64141 | 2 |
| C2×C3×#3753 | 2 |
| C3×#64117 | 2 |
| C3×#64116 | 2 |
| C33×#100 | 2 |
| C3×#63650 | 2 |
| C3×#63649 | 2 |
| #10592448 | 3 |
| C3×#4749 | 3 |