Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
386 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 68 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×C3×PSU(3,𝔽2) | C2 | semidirect |
| 2. C2×C3×AΓL(1,𝔽9) | C2 | semidirect |
| 4. C3×C22⋊AGL(1,𝔽9) | C2 | semidirect |
| 5. C3×PSU(3,𝔽2)⋊C4 | C2 | semidirect |
| 6. #10596418 | C3 | direct (N × H) |
| 18. C22×PSU(3,𝔽2) | C2×C3 | semidirect |
| 19. C2×AΓL(1,𝔽9) | C2×C3 | semidirect |
| 21. C22⋊AGL(1,𝔽9) | C2×C3 | semidirect |
| 22. PSU(3,𝔽2)⋊C4 | C2×C3 | semidirect |
| 32. C3×PSU(3,𝔽2) | D4 | semidirect |
| 51. C22×C33 | SD16 | semidirect |
| 54. C2×C3×C3⋊D3 | SD16 | semidirect |
| 79. PSU(3,𝔽2) | C3×D4 | semidirect |
| 113. C22×C32 | C3×SD16 | semidirect |
| 116. C2×C3⋊D3 | C3×SD16 | semidirect |
| 141. C33 | #448 | semidirect |
| 203. C22×C3 | AΓL(1,𝔽9) | semidirect |
| 220. C32 | C3×#448 | semidirect |
| 259. C22 | C3×AΓL(1,𝔽9) | semidirect |
| 266. C3 | #10596418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×PSU(3,𝔽2) | 2 |
| C2×C3×AΓL(1,𝔽9) | 2 |
| C3×#64242 | 2 |
| C3×C22⋊AGL(1,𝔽9) | 2 |
| C3×PSU(3,𝔽2)⋊C4 | 2 |
| #10596418 | 3 |
| C3×#448 | 9 |