Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
730 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 1. #11722673 | C2 | semidirect |
| 2. C3×C9×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #11721836 | C2 | semidirect |
| 4. #11721833 | C2 | semidirect |
| 5. #11720585 | C2 | semidirect |
| 6. #11720558 | C2 | semidirect |
| 7. #11720556 | C2 | semidirect |
| 35. C9×AGL(1,ℤ/8) | D3 | semidirect |
| 112. C3×AGL(1,ℤ/8) | D9 | semidirect |
| 232. AGL(1,ℤ/8) | C3⋊D9 | semidirect |
| 237. C3×C9 | #454 | semidirect |
| 332. C9 | #5201 | semidirect |
| 376. C3 | #10588881 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722673 | 2 |
| C3×C9×AGL(1,ℤ/8) | 2 |
| #11721836 | 2 |
| #11721833 | 2 |
| #11720585 | 2 |
| #11720558 | 2 |
| #11720556 | 2 |
| #10592900 | 3 |
| #10588881 | 3 |