Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
422 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. C2×C3×#3664 | C2 | semidirect |
| 3. #11720910 | C2 | semidirect |
| 4. C2×#88423 | C2 | semidirect |
| 5. #11720537 | C2 | semidirect |
| 6. C9×#821 | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 32. C2×#3664 | D3 | semidirect |
| 50. C3×Dic18 | D4 | semidirect |
| 96. C3⋊Dic9 | SD16 | semidirect |
| 109. #821 | D9 | semidirect |
| 148. Dic18 | #67 | semidirect |
| 226. C3×C9 | #460 | semidirect |
| 325. C9 | #5163 | semidirect |
| 370. C3 | #10588442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#3664 | 2 |
| #11721043 | 2 |
| #11720910 | 2 |
| C2×#88423 | 2 |
| #11720537 | 2 |
| C9×#821 | 2 |
| #11720266 | 2 |
| #10590876 | 3 |
| #10588442 | 3 |