Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
800 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 234 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×#125 | C2 | semidirect |
| 3. C32×#810 | C2 | semidirect |
| 5. C32×C4×C3⋊C8 | C2 | semidirect |
| 7. C3×#5068 | C3 | direct (N × H) |
| 16. C32×#125 | D3 | semidirect |
| 17. C32×#125 | C2×C3 | semidirect |
| 23. C3×#810 | C2×C3 | semidirect |
| 25. C3×C4×C3⋊C8 | C2×C3 | semidirect |
| 35. #5068 | C32 | direct (N × H) |
| 61. C3×#125 | C3×D3 | semidirect |
| 62. C3×#125 | C2×C32 | semidirect |
| 68. #810 | C2×C32 | semidirect |
| 70. C4×C3⋊C8 | C2×C32 | semidirect |
| 129. #125 | C32×D3 | semidirect |
| 134. C33 | #488 | semidirect |
| 188. C32 | #5068 | direct (N × H) |
| 189. C32 | C3×#488 | semidirect |
| 214. C3 | C3×#5068 | direct (N × H) |
| 215. C3 | C32×#488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#125 | 2 |
| C32×#875 | 2 |
| C32×#810 | 2 |
| C32×#809 | 2 |
| C32×C4×C3⋊C8 | 2 |
| C32×#488 | 3 |
| C3×#5068 | 3 |