Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
495 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 7. M16×H(3,𝔽3) | C4 | semidirect |
| 14. C2×#6180 | C4 | semidirect |
| 32. C32×M16 | Dic3 | semidirect |
| 102. H(3,𝔽3) | #344 | semidirect |
| 131. M16 | #1084 | semidirect |
| 155. C32 | #4559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×H(3,𝔽3) | 2 |
| #11721826 | 2 |
| C2×#88538 | 2 |
| C3×#4559 | 3 |