Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
270 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 89. C3×C9 | #362 | semidirect |
| 123. C9 | #4565 | semidirect |
| 139. C3 | #10588242 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| #11720535 | 2 |
| #11720534 | 2 |
| #10589431 | 3 |
| #10588242 | 3 |