Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 166. C3×C9 | #479 | semidirect |
| 225. C9 | #4829 | semidirect |
| 252. C3 | #10588511 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721707 | 2 |
| C4×#6226 | 2 |
| C3×C9×C4⋊C8 | 2 |
| #11720541 | 2 |
| #11720540 | 2 |
| #11720539 | 2 |
| #10592528 | 3 |
| #10588511 | 3 |