Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
434 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 3. #11720912 | C2 | semidirect |
| 5. #11720269 | C2 | semidirect |
| 6. #11720265 | C2 | semidirect |
| 7. Dic3×C9⋊C8 | C2 | semidirect |
| 13. #88543 | C4 | semidirect |
| 43. #6226 | C2×C4 | semidirect |
| 49. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 90. C9×Dic3 | SD16 | semidirect |
| 212. C3×C9 | C4×SD16 | semidirect |
| 301. Dic3 | #3672 | semidirect |
| 304. C9 | #4758 | semidirect |
| 343. C3 | C4×#3672 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88543 | 2 |
| D4×C9×Dic3 | 2 |
| #11720912 | 2 |
| C3×#63392 | 2 |
| #11720269 | 2 |
| #11720265 | 2 |
| Dic3×C9⋊C8 | 2 |
| #10591401 | 3 |
| C4×#3672 | 3 |