Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
386 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 118 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. C3×#63395 | C2 | semidirect |
| 5. C3×#63367 | C2 | semidirect |
| 7. #10588723 | C3 | direct (N × H) |
| 25. #63395 | C2×C3 | semidirect |
| 27. #63367 | C2×C3 | semidirect |
| 169. C3×C9 | #483 | semidirect |
| 246. C9 | C3×#483 | semidirect |
| 279. C3 | #10588723 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C22⋊Q8 | 2 |
| C2×C3×C4⋊Dic9 | 2 |
| C3×#63395 | 2 |
| C3×#63389 | 2 |
| C3×#63367 | 2 |
| C3×#5043 | 3 |
| #10588723 | 3 |