Finite Group DatabasebetaFinite Group Databasebeta← C22⋊C4×PSU(3,𝔽2)⋊C3 #72220406
Order 3456.
716 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 716 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. C2×C4×PSU(3,𝔽2)⋊C3 | C2 | semidirect |
| 3. C22⋊C4×PSU(3,𝔽2) | C3 | semidirect |
| 5. C22×PSU(3,𝔽2)⋊C3 | C4 | semidirect |
| 10. C2×C4×PSU(3,𝔽2) | C2×C3 | semidirect |
| 28. C22×PSU(3,𝔽2) | C3×C4 | semidirect |
| 39. PSU(3,𝔽2)⋊C3 | C22⋊C4 | direct (N × H) |
| 83. C32×C22⋊C4 | SL(2,𝔽3) | semidirect |
| 84. #3757 | SL(2,𝔽3) | semidirect |
| 85. #3752 | SL(2,𝔽3) | semidirect |
| 142. PSU(3,𝔽2) | C3×C22⋊C4 | semidirect |
| 145. C2×C32×C4 | C2×SL(2,𝔽3) | semidirect |
| 146. C2×C3⋊Dic3 | C2×SL(2,𝔽3) | semidirect |
| 185. C22×C32 | C4×SL(2,𝔽3) | semidirect |
| 191. C2×C3⋊D3 | C4×SL(2,𝔽3) | semidirect |
| 299. C22⋊C4 | PSU(3,𝔽2)⋊C3 | direct (N × H) |
| 336. C32 | C22⋊C4×SL(2,𝔽3) | semidirect |
| 366. C2×C4 | C2×PSU(3,𝔽2)⋊C3 | semidirect |
| 394. C22 | C4×PSU(3,𝔽2)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×PSU(3,𝔽2)⋊C3 | 2 |
| C2×C4×PSU(3,𝔽2)⋊C3 | 2 |
| C22⋊C4×PSU(3,𝔽2) | 3 |
| C22⋊C4×(C3⋊D3)⋊C3 | 4 |
| C22⋊C4×SL(2,𝔽3) | 9 |