Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
364 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 13. C3×Dic36 | C4 | semidirect |
| 55. Dic36 | Dic3 | semidirect |
| 136. C3×C9 | #441 | semidirect |
| 189. C9 | #5184 | semidirect |
| 211. C3 | #10588533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic36 | 2 |
| #11720910 | 2 |
| #11720538 | 2 |
| C9×#817 | 2 |
| #11720268 | 2 |
| #10590819 | 3 |
| #10588533 | 3 |