Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
502 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 102 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. D4×PSU(3,𝔽2) | C2 | semidirect |
| 3. D4×AGL(1,𝔽9) | C2 | semidirect |
| 4. #10596418 | C2 | semidirect |
| 5. #10596416 | C2 | semidirect |
| 6. #10596415 | C2 | semidirect |
| 7. C2×PSU(3,𝔽2)⋊C4 | C2 | semidirect |
| 8. #10596409 | C2 | semidirect |
| 9. C4×AΓL(1,𝔽9) | C2 | semidirect |
| 10. PSU(3,𝔽2)⋊Q8 | C2 | semidirect |
| 11. #10596404 | C2 | semidirect |
| 96. PSU(3,𝔽2) | #41 | semidirect |
| 102. C32×D4 | SD16 | semidirect |
| 103. #638 | SD16 | semidirect |
| 104. C4⋊(C3⋊D3) | SD16 | semidirect |
| 268. C32 | #3298 | semidirect |
| 284. D4 | AΓL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×PSU(3,𝔽2) | 2 |
| #10596519 | 2 |
| D4×AGL(1,𝔽9) | 2 |
| #10596418 | 2 |
| #10596416 | 2 |
| #10596415 | 2 |
| C2×PSU(3,𝔽2)⋊C4 | 2 |
| #10596409 | 2 |
| C4×AΓL(1,𝔽9) | 2 |
| PSU(3,𝔽2)⋊Q8 | 2 |
| #10596404 | 2 |
| #3298 | 9 |