Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
238 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 4. AGL(1,𝔽9)⋊C8 | C2 | direct (N × H) |
| 19. C2×AGL(1,𝔽9) | C8 | semidirect |
| 44. AGL(1,𝔽9) | C2×C8 | semidirect |
| 96. C2×C32 | #334 | semidirect |
| 98. C3⋊D3 | #334 | semidirect |
| 127. C32 | C2×#334 | semidirect |
| 169. C2 | AGL(1,𝔽9)⋊C8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×AGL(1,𝔽9) | 2 |
| C2×#63744 | 2 |
| C2×#63732 | 2 |
| AGL(1,𝔽9)⋊C8 | 2 |
| C2×#334 | 9 |