Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
646 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 215 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. #10596484 | C2 | direct (N × H) |
| 4. C2×C4⋊AGL(1,𝔽9) | C2 | semidirect |
| 5. C2×C4×AGL(1,𝔽9) | C2 | semidirect |
| 17. C4⋊AGL(1,𝔽9) | C22 | semidirect |
| 18. C4×AGL(1,𝔽9) | C22 | semidirect |
| 31. C22×C32×C4 | C8 | semidirect |
| 32. C22×C3⋊Dic3 | C8 | semidirect |
| 33. C2×C4×C3⋊D3 | C8 | semidirect |
| 34. C2×C4×C3⋊D3 | C8 | semidirect |
| 35. C2×C4×C3⋊D3 | C8 | semidirect |
| 69. C2×C32×C4 | C2×C8 | semidirect |
| 72. C2×C3⋊Dic3 | C2×C8 | semidirect |
| 75. C4×C3⋊D3 | C2×C8 | semidirect |
| 76. C4×C3⋊D3 | C2×C8 | semidirect |
| 147. C2×C32 | #431 | semidirect |
| 150. C3⋊D3 | #431 | semidirect |
| 170. C22×C4 | AGL(1,𝔽9) | semidirect |
| 195. C32 | C2×#431 | semidirect |
| 226. C2×C4 | C2×AGL(1,𝔽9) | semidirect |
| 262. C2 | #10596484 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#157 | 2 |
| C2×C22⋊AGL(1,𝔽9) | 2 |
| #10596484 | 2 |
| C2×C4⋊AGL(1,𝔽9) | 2 |
| C2×C4×AGL(1,𝔽9) | 2 |
| C2×#431 | 9 |