Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
308 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 2. C2×Dic36⋊C3 | C2 | semidirect |
| 3. #63386⋊C3 | C2 | direct (N × H) |
| 4. C2×3−1+2⋊C16 | C2 | semidirect |
| 6. C2×#63386 | C3 | semidirect |
| 13. Dic36⋊C3 | C22 | semidirect |
| 14. 3−1+2⋊C16 | C22 | semidirect |
| 21. C2×Dic36 | C2×C3 | semidirect |
| 22. #63386 | C2×C3 | semidirect |
| 23. C2×C9⋊C16 | C2×C3 | semidirect |
| 53. Dic36 | C22×C3 | semidirect |
| 54. C9⋊C16 | C22×C3 | semidirect |
| 95. C2×3−1+2 | SD32 | semidirect |
| 134. 3−1+2 | C2×SD32 | semidirect |
| 160. C2×C9 | C3×SD32 | semidirect |
| 184. C9 | C2×C3×SD32 | semidirect |
| 209. C2 | #63386⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×3−1+2 | 2 |
| C2×Dic36⋊C3 | 2 |
| #63386⋊C3 | 2 |
| C2×3−1+2⋊C16 | 2 |
| C2×C3×#827 | 3 |
| C2×#63386 | 3 |