Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
869 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 869 conjugacy classes of subgroups — too many to draw. Only its 221 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. #11721826 | C2 | semidirect |
| 3. C22×#6180 | C2 | semidirect |
| 4. #11720583 | C2 | semidirect |
| 5. #11720578 | C2 | semidirect |
| 8. #41×H(3,𝔽3) | C4 | semidirect |
| 42. C32×#41 | Dic3 | semidirect |
| 132. H(3,𝔽3) | #416 | semidirect |
| 168. #41 | #1084 | semidirect |
| 199. C32 | #5233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×H(3,𝔽3) | 2 |
| #11721826 | 2 |
| C22×#6180 | 2 |
| #11720583 | 2 |
| #11720578 | 2 |
| C3×#5233 | 3 |