Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
374 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
| 56. Dic36 | Dic3 | semidirect |
| 61. C3⋊Dic9 | Q16 | semidirect |
| 145. C3×C9 | C4×Q16 | semidirect |
| 207. C9 | Dic3×Q16 | semidirect |
| 234. C3 | #10588553 | 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 |
| C8×C3⋊Dic9 | 2 |
| C9×#818 | 2 |
| #11720268 | 2 |
| #10590818 | 3 |
| #10588553 | 3 |