Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
610 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 231 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 |
|---|---|---|
| 35. C3×C4×C9 | Q16 | semidirect |
| 72. C4×C9 | Dic12 | semidirect |
| 78. C3×C9 | #494 | semidirect |
| 100. C3×C4 | Dic36 | semidirect |
| 107. C9 | #4699 | semidirect |
| 119. C4 | #88521 | semidirect |
| 121. C3 | #10588365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88521 | 2 |
| #11721706 | 2 |
| C3×C4×C8×C9 | 2 |
| #10592398 | 3 |
| #10588365 | 3 |