Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
878 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 407 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 |
|---|---|---|
| 3. C2×C4×AGL(1,𝔽9) | C2 | direct (N × H) |
| 6. C22×AGL(1,𝔽9) | C4 | direct (N × H) |
| 11. C4×AGL(1,𝔽9) | C22 | direct (N × H) |
| 13. C22×#157 | C8 | semidirect |
| 18. C2×AGL(1,𝔽9) | C2×C4 | direct (N × H) |
| 20. C22×C32×C4 | C8 | semidirect |
| 21. C22×C3⋊Dic3 | C8 | semidirect |
| 22. C2×C4×C3⋊D3 | C8 | semidirect |
| 34. C2×#157 | C2×C8 | semidirect |
| 39. AGL(1,𝔽9) | C22×C4 | direct (N × H) |
| 40. C2×C32×C4 | C2×C8 | semidirect |
| 41. C2×C3⋊Dic3 | C2×C8 | semidirect |
| 42. C4×C3⋊D3 | C2×C8 | semidirect |
| 52. C22×C32 | C4×C8 | semidirect |
| 54. C2×C3⋊D3 | C4×C8 | semidirect |
| 60. #157 | C22×C8 | semidirect |
| 62. C32×C4 | C22×C8 | semidirect |
| 63. C3⋊Dic3 | C22×C8 | semidirect |
| 81. C2×C32 | C2×C4×C8 | semidirect |
| 83. C3⋊D3 | C2×C4×C8 | semidirect |
| 95. C22×C4 | AGL(1,𝔽9) | direct (N × H) |
| 109. C32 | C22×C4×C8 | semidirect |
| 124. C2×C4 | C2×AGL(1,𝔽9) | direct (N × H) |
| 136. C22 | C4×AGL(1,𝔽9) | direct (N × H) |
| 142. C4 | C22×AGL(1,𝔽9) | direct (N × H) |
| 147. C2 | C2×C4×AGL(1,𝔽9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×AGL(1,𝔽9) | 2 |
| C22×C4×#157 | 2 |
| C2×C4×AGL(1,𝔽9) | 2 |
| C22×C4×C8 | 9 |