Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
740 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 166 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. C2×C3×#3746 | C2 | semidirect |
| 3. C3×#63656 | C2 | semidirect |
| 4. C3×#63654 | C2 | semidirect |
| 5. C3×#63639 | C2 | semidirect |
| 6. #10592894 | C3 | direct (N × H) |
| 20. C2×#3746 | C2×C3 | semidirect |
| 22. #63656 | C2×C3 | semidirect |
| 23. #63654 | C2×C3 | semidirect |
| 24. #63639 | C2×C3 | semidirect |
| 156. C33 | #510 | semidirect |
| 220. C32 | #5195 | semidirect |
| 221. C32 | C3×#510 | semidirect |
| 248. C3 | C3×#5195 | semidirect |
| 249. C3 | #10592894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#135 | 2 |
| C2×C3×#3746 | 2 |
| C3×#63656 | 2 |
| C3×#63654 | 2 |
| C3×#63639 | 2 |
| #10592894 | 3 |
| C3×#5195 | 3 |