Finite Group DatabasebetaFinite Group Databasebeta← C3×C8×PSU(3,𝔽2)⋊C3 #72218924
Order 5184.
358 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 54 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. C3×C8×PSU(3,𝔽2) | C3 | semidirect |
| 3. C8×PSU(3,𝔽2)⋊C3 | C3 | direct (N × H) |
| 10. C3×PSU(3,𝔽2)⋊C3 | C8 | direct (N × H) |
| 14. C8×PSU(3,𝔽2) | C32 | semidirect |
| 34. C3×PSU(3,𝔽2) | C3×C8 | semidirect |
| 35. PSU(3,𝔽2)⋊C3 | C3×C8 | direct (N × H) |
| 41. C33×C8 | SL(2,𝔽3) | semidirect |
| 42. C3×C3⋊(C3⋊C8) | SL(2,𝔽3) | semidirect |
| 84. PSU(3,𝔽2) | C32×C8 | semidirect |
| 100. C32×C8 | C3×SL(2,𝔽3) | semidirect |
| 101. C3⋊(C3⋊C8) | C3×SL(2,𝔽3) | semidirect |
| 149. C33 | C8×SL(2,𝔽3) | semidirect |
| 167. C3×C8 | PSU(3,𝔽2)⋊C3 | direct (N × H) |
| 213. C32 | C3×C8×SL(2,𝔽3) | semidirect |
| 221. C8 | C3×PSU(3,𝔽2)⋊C3 | direct (N × H) |
| 243. C3 | C8×PSU(3,𝔽2)⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×PSU(3,𝔽2)⋊C3 | 2 |
| C3×C8×PSU(3,𝔽2) | 3 |
| C8×PSU(3,𝔽2)⋊C3 | 3 |
| C3×C8×(C3⋊D3)⋊C3 | 4 |
| C3×C8×SL(2,𝔽3) | 9 |