Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
581 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 581 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×SU(3,𝔽2) | C2 | semidirect |
| 3. C22×#6249 | C2 | semidirect |
| 4. C2×#6249⋊C2 | C2 | direct (N × H) |
| 9. C2×SU(3,𝔽2) | C22 | semidirect |
| 12. C2×#6249 | C22 | semidirect |
| 13. #6249⋊C2 | C22 | direct (N × H) |
| 22. SU(3,𝔽2) | C23 | semidirect |
| 25. #6249 | C23 | semidirect |
| 28. C22×H(3,𝔽3) | SD16 | semidirect |
| 29. C2×#272 | SD16 | semidirect |
| 47. C2×H(3,𝔽3) | C2×SD16 | semidirect |
| 48. #272 | C2×SD16 | semidirect |
| 72. H(3,𝔽3) | C22×SD16 | semidirect |
| 147. C22 | #6249⋊C2 | direct (N × H) |
| 156. C2 | C2×#6249⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SU(3,𝔽2) | 2 |
| C22×#1088⋊C2 | 2 |
| C22×#6249 | 2 |
| C2×#6249⋊C2 | 2 |
| C22×#215 | 9 |