Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
441 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 441 conjugacy classes of subgroups — too many to draw. Only its 74 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×C32×PSU(3,𝔽2) | C2 | semidirect |
| 3. C2×C3×C3⋊AGL(1,𝔽9) | C2 | semidirect |
| 4. C3×#89092 | C2 | direct (N × H) |
| 5. C2×#89092 | C3 | direct (N × H) |
| 11. C32×PSU(3,𝔽2) | C22 | semidirect |
| 14. C3×C3⋊AGL(1,𝔽9) | C22 | semidirect |
| 16. C2×C3×PSU(3,𝔽2) | D3 | semidirect |
| 17. C2×C3×PSU(3,𝔽2) | C2×C3 | semidirect |
| 20. C2×C3⋊AGL(1,𝔽9) | C2×C3 | semidirect |
| 22. #89092 | C2×C3 | direct (N × H) |
| 46. C3×PSU(3,𝔽2) | C2×D3 | semidirect |
| 47. C3×PSU(3,𝔽2) | C22×C3 | semidirect |
| 52. C3⋊AGL(1,𝔽9) | C22×C3 | semidirect |
| 54. C2×C34 | SD16 | semidirect |
| 56. C32×C3⋊D3 | SD16 | semidirect |
| 58. C2×PSU(3,𝔽2) | C3×D3 | semidirect |
| 93. C34 | C2×SD16 | semidirect |
| 101. PSU(3,𝔽2) | C2×C3×D3 | semidirect |
| 117. C2×C33 | #215 | semidirect |
| 118. C2×C33 | C3×SD16 | semidirect |
| 124. C3×C3⋊D3 | #215 | semidirect |
| 125. C3×C3⋊D3 | C3×SD16 | semidirect |
| 178. C33 | C2×#215 | semidirect |
| 179. C33 | C2×C3×SD16 | semidirect |
| 215. C2×C32 | C3×#215 | semidirect |
| 216. C2×C32 | AΓL(1,𝔽9) | semidirect |
| 218. C3⋊D3 | C3×#215 | semidirect |
| 275. C32 | C2×C3×#215 | semidirect |
| 276. C32 | C2×AΓL(1,𝔽9) | semidirect |
| 299. C2×C3 | C3×AΓL(1,𝔽9) | semidirect |
| 300. C2×C3 | #89092 | direct (N × H) |
| 318. C3 | C2×C3×AΓL(1,𝔽9) | semidirect |
| 319. C3 | C2×#89092 | direct (N × H) |
| 323. C2 | C3×#89092 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×PSU(3,𝔽2) | 2 |
| C2×C3×#157⋊D3 | 2 |
| C2×C3×C3⋊AGL(1,𝔽9) | 2 |
| C3×#89092 | 2 |
| C2×#89092 | 3 |
| C2×C3×AΓL(1,𝔽9) | 3 |
| C2×C3×#215 | 9 |