Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
352 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 4. C3×#4506 | C3 | direct (N × H) |
| 18. #4506 | C32 | direct (N × H) |
| 68. C33 | #368 | semidirect |
| 99. C32 | #4506 | direct (N × H) |
| 100. C32 | C3×#368 | semidirect |
| 115. C3 | C3×#4506 | direct (N × H) |
| 116. C3 | C32×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C16 | 2 |
| C32×#819 | 2 |
| C32×#368 | 3 |
| C3×#4506 | 3 |