Finite Group DatabasebetaFinite Group DatabasebetaOrder 3456.
358 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 43 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. Q8×PSU(3,𝔽2)⋊C3 | C2 | semidirect |
| 3. C8×PSU(3,𝔽2)⋊C3 | C2 | semidirect |
| 4. SD16×PSU(3,𝔽2) | C3 | semidirect |
| 9. Q8×PSU(3,𝔽2) | C2×C3 | semidirect |
| 15. C8×PSU(3,𝔽2) | C2×C3 | semidirect |
| 43. PSU(3,𝔽2)⋊C3 | SD16 | direct (N × H) |
| 80. C32×SD16 | SL(2,𝔽3) | semidirect |
| 81. #3755 | SL(2,𝔽3) | semidirect |
| 82. #3754 | SL(2,𝔽3) | semidirect |
| 83. #3744 | SL(2,𝔽3) | semidirect |
| 116. PSU(3,𝔽2) | C3×SD16 | semidirect |
| 119. C32×Q8 | C2×SL(2,𝔽3) | semidirect |
| 128. #634 | C2×SL(2,𝔽3) | semidirect |
| 138. C32×C8 | C2×SL(2,𝔽3) | semidirect |
| 139. C3⋊(C3⋊C8) | C2×SL(2,𝔽3) | semidirect |
| 262. SD16 | PSU(3,𝔽2)⋊C3 | direct (N × H) |
| 297. C32 | SD16×SL(2,𝔽3) | semidirect |
| 306. Q8 | C2×PSU(3,𝔽2)⋊C3 | semidirect |
| 320. C8 | C2×PSU(3,𝔽2)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×PSU(3,𝔽2)⋊C3 | 2 |
| D4×PSU(3,𝔽2)⋊C3 | 2 |
| C8×PSU(3,𝔽2)⋊C3 | 2 |
| SD16×PSU(3,𝔽2) | 3 |
| SD16×(C3⋊D3)⋊C3 | 4 |
| SD16×SL(2,𝔽3) | 9 |