Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 35. #6226 | Q8 | semidirect |
| 138. C3×C9 | #475 | semidirect |
| 191. C9 | #4851 | semidirect |
| 216. C3 | #10588515 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721706 | 2 |
| C4×#6226 | 2 |
| C3×C9×C4⋊C8 | 2 |
| #11720540 | 2 |
| #11720539 | 2 |
| #10592550 | 3 |
| #10588515 | 3 |