Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
341 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 2. H(3,𝔽3)×M32 | C2 | semidirect |
| 3. #11720552 | C2 | semidirect |
| 12. C32×M32 | D3 | semidirect |
| 69. M32 | #272 | semidirect |
| 71. H(3,𝔽3) | #361 | semidirect |
| 105. C32 | #4516 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88529 | 2 |
| H(3,𝔽3)×M32 | 2 |
| #11720552 | 2 |
| C3×#4516 | 3 |