Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
358 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 75 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. C3×#63471 | C2 | semidirect |
| 3. C2×#88416 | C2 | semidirect |
| 4. #11720858 | C2 | semidirect |
| 5. #11720557 | C2 | semidirect |
| 6. C9×#822 | C2 | semidirect |
| 7. #11720289 | C2 | semidirect |
| 32. #63471 | D3 | semidirect |
| 113. #822 | D9 | semidirect |
| 218. C3×C9 | #471 | semidirect |
| 306. C9 | #5203 | semidirect |
| 343. C3 | #10588578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63471 | 2 |
| #11720873 | 2 |
| C2×#88416 | 2 |
| #11720858 | 2 |
| #11720557 | 2 |
| C9×#822 | 2 |
| #11720289 | 2 |
| #10590985 | 3 |
| #10588578 | 3 |