Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
288 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 40 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×#63690 | C2 | semidirect |
| 3. C3×#63422 | C2 | semidirect |
| 5. #10589530 | C3 | direct (N × H) |
| 16. #63690 | C2×C3 | semidirect |
| 20. #63422 | C2×C3 | semidirect |
| 258. C3 | #10589530 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63700 | 2 |
| C3×#63690 | 2 |
| C3×#63422 | 2 |
| C3×#5242 | 3 |
| #10589530 | 3 |
| C3×#3674 | 4 |