Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
230 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 9. C3×C9×C16 | C4 | semidirect |
| 10. C3⋊(C9⋊C16) | C4 | semidirect |
| 32. C9×C16 | Dic3 | semidirect |
| 63. C3×C16 | Dic9 | semidirect |
| 78. C3×C9 | #347 | semidirect |
| 97. C16 | C3⋊Dic9 | semidirect |
| 107. C9 | #4512 | semidirect |
| 121. C3 | #10588189 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×M32 | 2 |
| #11720538 | 2 |
| #11720534 | 2 |
| #10589378 | 3 |
| #10588189 | 3 |