Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 24. #4699 | C9 | direct (N × H) |
| 38. C3×C4×C9 | Q16 | semidirect |
| 85. C4×C9 | Dic12 | semidirect |
| 90. C3×C9 | #494 | semidirect |
| 121. C3×C4 | C9×Q16 | semidirect |
| 128. C9 | #4699 | direct (N × H) |
| 142. C4 | C9×Dic12 | semidirect |
| 145. C3 | C9×#494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×Dic12 | 2 |
| C9×#869 | 2 |
| C3×C4×C8×C9 | 2 |
| C3×#4699 | 3 |
| C9×#494 | 3 |