Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #11721744 | C2 | semidirect |
| 5. #11720539 | C2 | semidirect |
| 6. #11720538 | C2 | semidirect |
| 7. #11720527 | C2 | semidirect |
| 182. C3×C9 | #489 | semidirect |
| 253. C9 | #4765 | semidirect |
| 287. C3 | #10588445 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721836 | 2 |
| #11721744 | 2 |
| C3×C9×#102 | 2 |
| #11720576 | 2 |
| #11720539 | 2 |
| #11720538 | 2 |
| #11720527 | 2 |
| #10592464 | 3 |
| #10588445 | 3 |