Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
864 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 170 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. C33×#137 | C2 | semidirect |
| 3. C3×#64157 | C2 | semidirect |
| 4. C2×C3×#3755 | C2 | semidirect |
| 5. C3×#63663 | C2 | semidirect |
| 6. C3×#63650 | C2 | semidirect |
| 7. C3×#63649 | C2 | semidirect |
| 8. #10592902 | C3 | direct (N × H) |
| 26. C32×#137 | D3 | semidirect |
| 27. C32×#137 | C2×C3 | semidirect |
| 29. #64157 | C2×C3 | semidirect |
| 30. C2×#3755 | C2×C3 | semidirect |
| 34. #63663 | C2×C3 | semidirect |
| 35. #63650 | C2×C3 | semidirect |
| 36. #63649 | C2×C3 | semidirect |
| 102. C3×#137 | C3×D3 | semidirect |
| 103. C3×#137 | C3⋊D3 | semidirect |
| 219. #137 | C3×C3⋊D3 | semidirect |
| 226. C33 | #471 | semidirect |
| 317. C32 | #5203 | semidirect |
| 318. C32 | C3×#471 | semidirect |
| 355. C3 | C3×#5203 | semidirect |
| 356. C3 | #10592902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#137 | 2 |
| C3×#64158 | 2 |
| C3×#64157 | 2 |
| C2×C3×#3755 | 2 |
| C3×#63663 | 2 |
| C3×#63650 | 2 |
| C3×#63649 | 2 |
| #10592902 | 3 |
| C3×#5203 | 3 |