Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
350 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 98 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. C3×#63450 | C2 | semidirect |
| 5. C3×#63376 | C2 | semidirect |
| 6. C3×#63375 | C2 | semidirect |
| 7. C3×#63368 | C2 | semidirect |
| 9. #10588445 | C3 | direct (N × H) |
| 29. #63450 | C2×C3 | semidirect |
| 33. #63376 | C2×C3 | semidirect |
| 34. #63375 | C2×C3 | semidirect |
| 35. #63368 | C2×C3 | semidirect |
| 203. C3×C9 | #489 | semidirect |
| 292. C9 | C3×#489 | semidirect |
| 331. C3 | #10588445 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63498 | 2 |
| C3×#63450 | 2 |
| C3×C9×#102 | 2 |
| C3×#63392 | 2 |
| C3×#63376 | 2 |
| C3×#63375 | 2 |
| C3×#63368 | 2 |
| C3×#4765 | 3 |
| #10588445 | 3 |