Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
234 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 8. C3×C9×Q16 | C4 | semidirect |
| 27. #4564 | C9 | direct (N × H) |
| 39. C9×Q16 | Dic3 | semidirect |
| 87. C3×Q16 | C4×C9 | semidirect |
| 113. C3×C9 | #358 | semidirect |
| 145. Q16 | C9×Dic3 | semidirect |
| 165. C9 | #4564 | direct (N × H) |
| 188. C3 | C9×#358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| C9×#818 | 2 |
| C2×C9×C3⋊C16 | 2 |
| C3×#4564 | 3 |
| C9×#358 | 3 |