Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1045 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 1045 conjugacy classes of subgroups — too many to draw. Only its 249 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. C2×#88538 | C2 | semidirect |
| 3. #11720573 | C2 | semidirect |
| 12. C2×#6180 | C22 | semidirect |
| 43. C22×H(3,𝔽3) | M16 | semidirect |
| 91. C22×C32 | #208 | semidirect |
| 100. H(3,𝔽3) | #407 | semidirect |
| 157. C32 | #5207 | semidirect |
| 182. C22 | #88538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×H(3,𝔽3) | 2 |
| C2×#88538 | 2 |
| #11720573 | 2 |
| C3×#5207 | 3 |