Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
605 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 605 conjugacy classes of subgroups — too many to draw. Only its 161 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. M16×H(3,𝔽3) | C4 | semidirect |
| 11. C4⋊#1084 | C4 | semidirect |
| 14. C4×#1084 | C4 | semidirect |
| 34. C32×M16 | Dic3 | semidirect |
| 106. H(3,𝔽3) | #339 | semidirect |
| 136. M16 | #1084 | semidirect |
| 163. C32 | #4555 | 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×C4×#1084 | 2 |
| C3×#4555 | 3 |