Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
240 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 2. C33×C32 | C2 | semidirect |
| 3. C32×C3⋊C32 | C2 | semidirect |
| 5. C3×#4447 | C3 | direct (N × H) |
| 13. C32×C32 | D3 | semidirect |
| 14. C32×C32 | C2×C3 | semidirect |
| 15. C3×C3⋊C32 | C2×C3 | semidirect |
| 20. #4447 | C32 | direct (N × H) |
| 35. C3×C32 | C3×D3 | semidirect |
| 36. C3×C32 | C2×C32 | semidirect |
| 37. C3⋊C32 | C2×C32 | semidirect |
| 64. C32 | C32×D3 | semidirect |
| 65. C33 | M64 | semidirect |
| 89. C32 | #4447 | direct (N × H) |
| 90. C32 | C3×M64 | semidirect |
| 103. C3 | C3×#4447 | direct (N × H) |
| 104. C3 | C32×M64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D3×C16 | 2 |
| C33×C32 | 2 |
| C32×C3⋊C32 | 2 |
| C32×M64 | 3 |
| C3×#4447 | 3 |