Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
266 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 62 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. #11724242 | C2 | semidirect |
| 3. C3×#64218 | C2 | semidirect |
| 4. #11724094 | C2 | semidirect |
| 5. #11724092 | C2 | semidirect |
| 14. C3⋊#3771 | C22 | semidirect |
| 15. C3×#3771 | C22 | semidirect |
| 18. #64218 | D3 | semidirect |
| 42. #3771 | C2×D3 | semidirect |
| 79. C3⋊(C3⋊D3) | M32 | semidirect |
| 115. C33 | C2×M32 | semidirect |
| 178. C32 | D3×M32 | semidirect |
| 212. C3 | #10596481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88924 | 2 |
| #11724242 | 2 |
| C3×#64218 | 2 |
| #11724094 | 2 |
| #11724092 | 2 |
| #10596481 | 3 |
| D3×M32 | 9 |