Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
436 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 158 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 |
|---|---|---|
| 3. #10589332 | C3 | direct (N × H) |
| 8. C3×C3⋊(C3⋊C16) | C4 | semidirect |
| 29. C3⋊(C3⋊C16) | C3×C4 | semidirect |
| 80. C33 | #347 | semidirect |
| 116. C32 | #4466 | semidirect |
| 117. C32 | C3×#347 | semidirect |
| 133. C3 | C3×#4466 | semidirect |
| 134. C3 | #10589332 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#97 | 2 |
| C3×#63639 | 2 |
| #10589332 | 3 |
| C3×#4466 | 3 |