Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 63. C3×C4×C9 | Q16 | semidirect |
| 135. C4×C9 | Dic12 | semidirect |
| 146. C3×C9 | #462 | semidirect |
| 189. C3×C4 | Dic36 | semidirect |
| 202. C9 | #4849 | semidirect |
| 225. C4 | #88521 | semidirect |
| 228. C3 | #10588513 | 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 |
| C4×#6226 | 2 |
| C3×C9×C4⋊C8 | 2 |
| #11720539 | 2 |
| #10592548 | 3 |
| #10588513 | 3 |