Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
628 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 628 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 |
|---|---|---|
| 5. C3×#4473 | C3 | direct (N × H) |
| 7. C2×C32×Dic6 | C4 | semidirect |
| 12. C32×C4×Dic3 | C4 | semidirect |
| 30. #4473 | C32 | direct (N × H) |
| 35. C2×C3×Dic6 | C3×C4 | semidirect |
| 46. C3×C4×Dic3 | C3×C4 | semidirect |
| 96. C2×Dic6 | C32×C4 | semidirect |
| 107. C4×Dic3 | C32×C4 | semidirect |
| 138. C33 | #354 | semidirect |
| 209. C32 | #4473 | direct (N × H) |
| 210. C32 | C3×#354 | semidirect |
| 243. C3 | C3×#4473 | direct (N × H) |
| 244. C3 | C32×#354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#936 | 2 |
| C33×#99 | 2 |
| C32×#834 | 2 |
| C32×#354 | 3 |
| C3×#4473 | 3 |