Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
932 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 214 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. C2×C3×#3746 | C2 | semidirect |
| 4. C3×#63644 | C2 | semidirect |
| 5. C3×#63643 | C2 | semidirect |
| 6. #10592836 | C3 | direct (N × H) |
| 21. C2×#3746 | C2×C3 | semidirect |
| 24. #63644 | C2×C3 | semidirect |
| 25. #63643 | C2×C3 | semidirect |
| 164. C33 | #470 | semidirect |
| 235. C32 | #5137 | semidirect |
| 236. C32 | C3×#470 | semidirect |
| 266. C3 | C3×#5137 | semidirect |
| 267. C3 | #10592836 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| C3×#64133 | 2 |
| C2×C3×#3746 | 2 |
| C3×#63644 | 2 |
| C3×#63643 | 2 |
| #10592836 | 3 |
| C3×#5137 | 3 |