Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
500 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 151 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. #11721706 | C2 | semidirect |
| 3. #11720582 | C2 | semidirect |
| 5. #11720516 | C2 | semidirect |
| 142. C3×C9 | #489 | semidirect |
| 199. C9 | #5055 | semidirect |
| 227. C3 | #10588734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#124 | 2 |
| #11721706 | 2 |
| #11720582 | 2 |
| #11720576 | 2 |
| #11720516 | 2 |
| #10592754 | 3 |
| #10588734 | 3 |