Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
286 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 5. C2×C3×Q8×C9 | C4 | semidirect |
| 8. C3×C42×C9 | C4 | semidirect |
| 23. #4541 | C9 | direct (N × H) |
| 30. C2×Q8×C9 | Dic3 | semidirect |
| 37. C42×C9 | Dic3 | semidirect |
| 75. C2×C3×Q8 | C4×C9 | semidirect |
| 85. C3×C42 | C4×C9 | semidirect |
| 110. C3×C9 | #354 | semidirect |
| 140. C2×Q8 | C9×Dic3 | semidirect |
| 144. C42 | C9×Dic3 | semidirect |
| 167. C9 | #4541 | direct (N × H) |
| 192. C3 | C9×#354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#124 | 2 |
| C9×#834 | 2 |
| C3×#4541 | 3 |
| C9×#354 | 3 |