Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
370 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 12. C4⋊AGL(1,𝔽9) | C4 | direct (N × H) |
| 28. C4×#157 | C8 | semidirect |
| 32. C32×C42 | C8 | semidirect |
| 33. C4×C3⋊Dic3 | C8 | semidirect |
| 34. C4×C3⋊Dic3 | C8 | semidirect |
| 35. C4×C3⋊Dic3 | C8 | semidirect |
| 85. #157 | C4⋊C8 | semidirect |
| 89. C32×C4 | C4×C8 | semidirect |
| 90. C32×C4 | C4⋊C8 | semidirect |
| 92. C3⋊Dic3 | C4×C8 | semidirect |
| 93. C3⋊Dic3 | C4⋊C8 | semidirect |
| 144. C42 | AGL(1,𝔽9) | semidirect |
| 158. C32 | C4×C4⋊C8 | semidirect |
| 209. C4 | C4×AGL(1,𝔽9) | semidirect |
| 210. C4 | 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 |
|---|---|
| C2×C4⋊AGL(1,𝔽9) | 2 |
| C2×C4×AGL(1,𝔽9) | 2 |
| C42×#157 | 2 |
| #10593267 | 2 |
| C4×C4⋊C8 | 9 |