Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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. C3×C9×C22⋊C8 | C2 | semidirect |
| 3. #11720572 | C2 | semidirect |
| 9. C2×C4⋊(C3⋊D9) | C4 | semidirect |
| 12. C4⋊(C3⋊Dic9) | C4 | semidirect |
| 17. C9×C22⋊C8 | D3 | semidirect |
| 62. C3×C22⋊C8 | D9 | semidirect |
| 138. C22⋊C8 | C3⋊D9 | semidirect |
| 140. C3×C9 | #327 | semidirect |
| 211. C9 | #4470 | semidirect |
| 249. C3 | #10588147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721819 | 2 |
| C3×C9×C22⋊C8 | 2 |
| #11720572 | 2 |
| #10589336 | 3 |
| #10588147 | 3 |