Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
520 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 4. #11720527 | C2 | semidirect |
| 5. #11720525 | C2 | semidirect |
| 142. C3×C9 | #484 | semidirect |
| 199. C9 | #4970 | semidirect |
| 227. C3 | #10588646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×C4⋊C4 | 2 |
| #11721813 | 2 |
| #11720571 | 2 |
| #11720527 | 2 |
| #11720525 | 2 |
| #10592669 | 3 |
| #10588646 | 3 |