Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1463 conjugacy classes of subgroups; only the 301 normal subgroups are shown.
This group has 1463 conjugacy classes of subgroups — too many to draw. Only its 301 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 |
|---|---|---|
| 4. #11721755 | C2 | semidirect |
| 6. C4×#6229 | C2 | semidirect |
| 10. C2×#6229 | C4 | semidirect |
| 126. H(3,𝔽3) | #519 | semidirect |
| 179. C32 | #5516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6229 | 2 |
| H(3,𝔽3)×#117 | 2 |
| #11721826 | 2 |
| #11721755 | 2 |
| #11721733 | 2 |
| C4×#6229 | 2 |
| C3×#5516 | 3 |