Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
868 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 868 conjugacy classes of subgroups — too many to draw. Only its 170 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×#64309 | C2 | semidirect |
| 2. C3×#64287 | C2 | semidirect |
| 3. C2×C3×#3776 | C2 | semidirect |
| 4. C3×#64239 | C2 | semidirect |
| 5. C3×#64237 | C2 | semidirect |
| 6. C3×#64228 | C2 | semidirect |
| 7. C3×#64226 | C2 | semidirect |
| 8. C3×#64223 | C2 | semidirect |
| 9. #10596516 | C3 | direct (N × H) |
| 30. #64309 | C2×C3 | semidirect |
| 31. #64287 | C2×C3 | semidirect |
| 32. C2×#3776 | C2×C3 | semidirect |
| 33. #64239 | C2×C3 | semidirect |
| 34. #64237 | C2×C3 | semidirect |
| 35. #64228 | C2×C3 | semidirect |
| 36. #64226 | C2×C3 | semidirect |
| 37. #64223 | C2×C3 | semidirect |
| 221. C33 | #578 | semidirect |
| 326. C32 | C3×#578 | semidirect |
| 368. C3 | #10596516 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64309 | 2 |
| C3×#64287 | 2 |
| C2×C3×#3776 | 2 |
| C3×#64239 | 2 |
| C3×#64237 | 2 |
| C3×#64228 | 2 |
| C3×#64226 | 2 |
| C3×#64223 | 2 |
| #10596516 | 3 |
| C3×#578 | 9 |