Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
430 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 109. C3×C9 | #499 | semidirect |
| 146. C9 | #4858 | semidirect |
| 163. C3 | #10588538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721746 | 2 |
| C3×C9×#106 | 2 |
| #11720540 | 2 |
| C8×C3⋊Dic9 | 2 |
| #11720525 | 2 |
| #10592557 | 3 |
| #10588538 | 3 |