Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
566 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 104 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. #10596542 | C2 | semidirect |
| 3. #10596484 | C2 | semidirect |
| 5. #10596415 | C2 | semidirect |
| 6. #10596409 | C2 | semidirect |
| 7. C4×AΓL(1,𝔽9) | C2 | semidirect |
| 8. GO+(4,𝔽2)⋊Q8 | C2 | semidirect |
| 16. C4⋊PSU(3,𝔽2) | C22 | semidirect |
| 17. C4⋊PSU(3,𝔽2) | C22 | semidirect |
| 19. C4×PSU(3,𝔽2) | C22 | semidirect |
| 28. C4⋊AGL(1,𝔽9) | C22 | semidirect |
| 29. C4×AGL(1,𝔽9) | C22 | semidirect |
| 30. AGL(1,𝔽9)⋊C4 | C22 | semidirect |
| 31. PSU(3,𝔽2)⋊C4 | C22 | semidirect |
| 89. C2×C32×C4 | SD16 | semidirect |
| 90. C2×C3⋊Dic3 | SD16 | semidirect |
| 91. C4×C3⋊D3 | SD16 | semidirect |
| 92. C4×C3⋊D3 | SD16 | semidirect |
| 249. C32 | #3101 | semidirect |
| 281. C2×C4 | AΓL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596542 | 2 |
| C2×C4×GO+(4,𝔽2) | 2 |
| #10596484 | 2 |
| #10596417 | 2 |
| #10596415 | 2 |
| #10596409 | 2 |
| C4×AΓL(1,𝔽9) | 2 |
| GO+(4,𝔽2)⋊Q8 | 2 |
| #3101 | 9 |