Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
552 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10593737 | C3 | direct (N × H) |
| 6. C33×C42 | C4 | semidirect |
| 7. C3×C4×C3⋊Dic3 | C4 | semidirect |
| 22. C32×C42 | C3×C4 | semidirect |
| 23. C4×C3⋊Dic3 | C3×C4 | semidirect |
| 52. C3×C42 | #157 | semidirect |
| 67. C33 | #383 | semidirect |
| 86. C42 | C3×#157 | semidirect |
| 100. C32 | C3×#383 | semidirect |
| 118. C3 | #10593737 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C42×C3⋊D3 | 2 |
| C3×#63781 | 2 |
| #10593737 | 3 |
| C3×#383 | 9 |