Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 88. C3⋊Dic9 | Q16 | semidirect |
| 188. C3×C9 | #462 | semidirect |
| 257. C9 | #5182 | semidirect |
| 288. C3 | #10588862 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| Q8×C3⋊Dic9 | 2 |
| #11721854 | 2 |
| C2×#88547 | 2 |
| #11720582 | 2 |
| #11720539 | 2 |
| #11720537 | 2 |
| #10592881 | 3 |
| #10588862 | 3 |