Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
896 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 896 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. C2×C33×SD16 | C2 | semidirect |
| 2. C3×#64151 | C2 | semidirect |
| 4. C3×#64110 | C2 | semidirect |
| 5. C3×#63663 | C2 | semidirect |
| 6. C3×#63660 | C2 | semidirect |
| 7. C3×#63646 | C2 | semidirect |
| 8. #10592876 | C3 | direct (N × H) |
| 26. C2×C32×SD16 | D3 | semidirect |
| 27. C2×C32×SD16 | C2×C3 | semidirect |
| 28. #64151 | C2×C3 | semidirect |
| 30. #64110 | C2×C3 | semidirect |
| 34. #63663 | C2×C3 | semidirect |
| 35. #63660 | C2×C3 | semidirect |
| 36. #63646 | C2×C3 | semidirect |
| 104. C2×C3×SD16 | C3×D3 | semidirect |
| 105. C2×C3×SD16 | C3⋊D3 | semidirect |
| 221. C2×SD16 | C3×C3⋊D3 | semidirect |
| 226. C33 | #471 | semidirect |
| 317. C32 | #5177 | semidirect |
| 318. C32 | C3×#471 | semidirect |
| 355. C3 | C3×#5177 | semidirect |
| 356. C3 | #10592876 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×SD16 | 2 |
| C3×#64151 | 2 |
| C3×#64141 | 2 |
| C3×#64110 | 2 |
| C3×#63663 | 2 |
| C3×#63660 | 2 |
| C3×#63646 | 2 |
| #10592876 | 3 |
| C3×#5177 | 3 |