Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
231 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 231 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 8. C16×H(3,𝔽3) | C4 | semidirect |
| 22. C32×C16 | Dic3 | semidirect |
| 56. H(3,𝔽3) | #365 | semidirect |
| 72. C16 | #1084 | semidirect |
| 81. C32 | #4513 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×M32 | 2 |
| #11720552 | 2 |
| #11720550 | 2 |
| C3×#4513 | 3 |