Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
502 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 5. AGL(1,𝔽9)⋊Q8 | C2 | direct (N × H) |
| 25. C2×AGL(1,𝔽9) | Q8 | semidirect |
| 52. AGL(1,𝔽9) | C2×Q8 | semidirect |
| 112. C2×C32 | #498 | semidirect |
| 114. C3⋊D3 | #498 | semidirect |
| 147. C32 | C2×#498 | semidirect |
| 188. C2 | AGL(1,𝔽9)⋊Q8 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊PSU(3,𝔽2) | 2 |
| C2×#64222 | 2 |
| C2×C4×AGL(1,𝔽9) | 2 |
| C2×AGL(1,𝔽9)⋊C4 | 2 |
| AGL(1,𝔽9)⋊Q8 | 2 |
| C2×#498 | 9 |