Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
540 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 14. #88547 | C4 | semidirect |
| 177. C3×C9 | #441 | semidirect |
| 241. C9 | #4789 | semidirect |
| 270. C3 | #10588469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C3⋊Dic9 | 2 |
| C2×#88547 | 2 |
| #11721743 | 2 |
| C3×C9×#103 | 2 |
| #11720539 | 2 |
| #11720538 | 2 |
| #11720526 | 2 |
| #10592488 | 3 |
| #10588469 | 3 |