Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
392 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 101 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×C3×C4⋊Dic9 | C2 | semidirect |
| 3. #11720571 | C2 | semidirect |
| 4. #11720294 | C2 | semidirect |
| 5. #11720265 | C2 | semidirect |
| 23. C2×C4⋊Dic9 | D3 | semidirect |
| 169. C3×C9 | #481 | semidirect |
| 250. C9 | #4968 | semidirect |
| 288. C3 | #10588714 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#930 | 2 |
| C2×C3×C4⋊Dic9 | 2 |
| #11720571 | 2 |
| #11720294 | 2 |
| #11720265 | 2 |
| #10591091 | 3 |
| #10588714 | 3 |