Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
302 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 125. C3×C9 | #499 | semidirect |
| 173. C9 | #4858 | semidirect |
| 193. C3 | #10588538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11720937 | 2 |
| C8×C3⋊Dic9 | 2 |
| C9×#817 | 2 |
| C3×#63377 | 2 |
| #11720263 | 2 |
| #10590874 | 3 |
| #10588538 | 3 |