Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
440 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 114 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×#63506 | C2 | semidirect |
| 3. C2×C3×#3674 | C2 | semidirect |
| 6. C2×C3×Dic36 | C2 | semidirect |
| 7. C3×#63375 | C2 | semidirect |
| 9. #10588847 | C3 | direct (N × H) |
| 32. #63506 | C2×C3 | semidirect |
| 33. C2×#3674 | C2×C3 | semidirect |
| 36. C2×Dic36 | C2×C3 | semidirect |
| 37. #63375 | C2×C3 | semidirect |
| 215. C3×C9 | #497 | semidirect |
| 304. C9 | C3×#497 | semidirect |
| 340. C3 | #10588847 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×SD16 | 2 |
| C3×#63506 | 2 |
| C2×C3×#3674 | 2 |
| C3×#63498 | 2 |
| C2×C3×#3672 | 2 |
| C2×C3×Dic36 | 2 |
| C3×#63375 | 2 |
| C3×#5167 | 3 |
| #10588847 | 3 |