Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
451 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 451 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. C2×#88530 | C2 | semidirect |
| 3. H(3,𝔽3)×M32 | C2 | semidirect |
| 4. #11720514 | C2 | semidirect |
| 5. #11720513 | C2 | semidirect |
| 18. C32×M32 | D3 | semidirect |
| 100. M32 | #272 | semidirect |
| 101. H(3,𝔽3) | #510 | semidirect |
| 146. C32 | #4909 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88530 | 2 |
| #11721779 | 2 |
| H(3,𝔽3)×M32 | 2 |
| #11720514 | 2 |
| #11720513 | 2 |
| C3×#4909 | 3 |