Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
164 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 93 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. C9×C3⋊C16 | C4 | semidirect |
| 24. #4512 | C9 | direct (N × H) |
| 36. C9×C16 | Dic3 | semidirect |
| 73. C3×C16 | C4×C9 | semidirect |
| 75. C3⋊C16 | C4×C9 | semidirect |
| 90. C3×C9 | #347 | semidirect |
| 114. C16 | C9×Dic3 | semidirect |
| 128. C9 | #4512 | direct (N × H) |
| 145. C3 | C9×#347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×M32 | 2 |
| C9×#815 | 2 |
| C9×#812 | 2 |
| C3×#4512 | 3 |
| C9×#347 | 3 |