Finite Group DatabasebetaFinite Group Databasebeta← C2×C8×PSU(3,𝔽2)⋊C3 #72244873
Order 3456.
408 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 71 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. C8×PSU(3,𝔽2)⋊C3 | C2 | direct (N × H) |
| 3. C2×C8×PSU(3,𝔽2) | C3 | semidirect |
| 12. C8×PSU(3,𝔽2) | C2×C3 | semidirect |
| 13. C2×PSU(3,𝔽2)⋊C3 | C8 | direct (N × H) |
| 35. PSU(3,𝔽2)⋊C3 | C2×C8 | direct (N × H) |
| 51. C2×PSU(3,𝔽2) | C3×C8 | semidirect |
| 67. C2×C32×C8 | SL(2,𝔽3) | semidirect |
| 68. C2×C3⋊(C3⋊C8) | SL(2,𝔽3) | semidirect |
| 69. C8×C3⋊D3 | SL(2,𝔽3) | semidirect |
| 101. PSU(3,𝔽2) | C2×C3×C8 | semidirect |
| 118. C32×C8 | C2×SL(2,𝔽3) | semidirect |
| 119. C3⋊(C3⋊C8) | C2×SL(2,𝔽3) | semidirect |
| 209. C2×C32 | C8×SL(2,𝔽3) | semidirect |
| 211. C3⋊D3 | C8×SL(2,𝔽3) | semidirect |
| 230. C2×C8 | PSU(3,𝔽2)⋊C3 | direct (N × H) |
| 261. C32 | C2×C8×SL(2,𝔽3) | semidirect |
| 282. C8 | C2×PSU(3,𝔽2)⋊C3 | direct (N × H) |
| 315. C2 | 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 |
|---|---|
| C2×C4×PSU(3,𝔽2)⋊C3 | 2 |
| C8×PSU(3,𝔽2)⋊C3 | 2 |
| C2×C8×PSU(3,𝔽2) | 3 |
| C2×C8×(C3⋊D3)⋊C3 | 4 |
| C2×C8×SL(2,𝔽3) | 9 |