Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
148 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 82. C3×C9 | #368 | semidirect |
| 117. C9 | #4493 | semidirect |
| 133. C3 | #10588170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3⋊(C9⋊C16) | 2 |
| C9×#819 | 2 |
| C3×#63372 | 2 |
| #10589144 | 3 |
| #10588170 | 3 |