Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
262 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 7. C2×C3×Dic18 | C4 | semidirect |
| 12. C3×C4×Dic9 | C4 | semidirect |
| 40. C2×Dic18 | Dic3 | semidirect |
| 46. C4×Dic9 | Dic3 | semidirect |
| 138. C3×C9 | #354 | semidirect |
| 210. C9 | #4541 | semidirect |
| 243. C3 | #10588149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63498 | 2 |
| #11720577 | 2 |
| C9×#834 | 2 |
| #10589180 | 3 |
| #10588149 | 3 |