Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
580 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 580 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. #10596545 | C2 | semidirect |
| 3. D4×AGL(1,𝔽9) | C2 | semidirect |
| 4. #10596417 | C2 | semidirect |
| 5. #10596416 | C2 | semidirect |
| 6. #10596412 | C2 | semidirect |
| 7. C2×GO+(4,𝔽2)⋊C4 | C2 | semidirect |
| 8. #10596410 | C2 | semidirect |
| 9. C4×AΓL(1,𝔽9) | C2 | semidirect |
| 10. GO+(4,𝔽2)⋊Q8 | C2 | semidirect |
| 11. #10596402 | C2 | semidirect |
| 13. C22×AGL(1,𝔽9) | C22 | semidirect |
| 15. C2×AΓL(1,𝔽9) | C22 | semidirect |
| 20. C22⋊PSU(3,𝔽2) | C22 | semidirect |
| 21. C2×#3777 | C22 | semidirect |
| 22. C4⋊PSU(3,𝔽2) | C22 | semidirect |
| 23. C4×PSU(3,𝔽2) | C22 | semidirect |
| 30. C22⋊AGL(1,𝔽9) | C22 | semidirect |
| 31. C4⋊AGL(1,𝔽9) | C22 | semidirect |
| 32. C4×AGL(1,𝔽9) | C22 | semidirect |
| 33. AGL(1,𝔽9)⋊C4 | C22 | semidirect |
| 34. AGL(1,𝔽9)⋊C4 | C22 | semidirect |
| 35. PSU(3,𝔽2)⋊C4 | C22 | semidirect |
| 38. GO+(4,𝔽2)⋊C4 | C22 | semidirect |
| 39. GO+(4,𝔽2)⋊C4 | C22 | semidirect |
| 40. GO+(4,𝔽2)⋊C4 | C22 | semidirect |
| 109. C32×D4 | SD16 | semidirect |
| 110. #638 | SD16 | semidirect |
| 111. C4⋊(C3⋊D3) | SD16 | semidirect |
| 285. C32 | #3295 | semidirect |
| 308. D4 | AΓL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596545 | 2 |
| D4×GO+(4,𝔽2) | 2 |
| D4×AGL(1,𝔽9) | 2 |
| #10596417 | 2 |
| #10596416 | 2 |
| #10596412 | 2 |
| C2×GO+(4,𝔽2)⋊C4 | 2 |
| #10596410 | 2 |
| C4×AΓL(1,𝔽9) | 2 |
| GO+(4,𝔽2)⋊Q8 | 2 |
| #10596402 | 2 |
| #3295 | 9 |