Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
380 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×#88524 | C2 | semidirect |
| 2. C3×#63464 | C2 | semidirect |
| 4. #11720869 | C2 | semidirect |
| 5. C9×#819 | C2 | semidirect |
| 6. #11720290 | C2 | semidirect |
| 7. #11720288 | C2 | semidirect |
| 36. #63464 | D3 | semidirect |
| 115. #819 | D9 | semidirect |
| 226. C3×C9 | #471 | semidirect |
| 318. C9 | #5141 | semidirect |
| 355. C3 | #10588578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| C3×#63464 | 2 |
| #11720873 | 2 |
| #11720869 | 2 |
| C9×#819 | 2 |
| #11720290 | 2 |
| #11720288 | 2 |
| #10590931 | 3 |
| #10588578 | 3 |