Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
758 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 758 conjugacy classes of subgroups — too many to draw. Only its 287 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) |
| 11. C4⋊AGL(1,𝔽9) | C22 | direct (N × H) |
| 21. C22×C32×C4 | C8 | semidirect |
| 22. C22×C3⋊Dic3 | C8 | semidirect |
| 23. C2×C4×C3⋊D3 | C8 | semidirect |
| 42. C2×C32×C4 | C2×C8 | semidirect |
| 43. C2×C3⋊Dic3 | C2×C8 | semidirect |
| 44. C4×C3⋊D3 | C2×C8 | semidirect |
| 54. C22×C32 | C4⋊C8 | semidirect |
| 56. C2×C3⋊D3 | C4⋊C8 | semidirect |
| 65. C32×C4 | C22×C8 | semidirect |
| 66. C3⋊Dic3 | C22×C8 | semidirect |
| 84. C2×C32 | C2×C4⋊C8 | semidirect |
| 86. C3⋊D3 | C2×C4⋊C8 | semidirect |
| 99. C22×C4 | AGL(1,𝔽9) | semidirect |
| 113. C32 | C22×C4⋊C8 | semidirect |
| 129. C2×C4 | C2×AGL(1,𝔽9) | semidirect |
| 141. C22 | C4⋊AGL(1,𝔽9) | direct (N × H) |
| 148. C4 | C22×AGL(1,𝔽9) | semidirect |
| 153. 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 |