Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
450 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 119 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 | semidirect |
| 5. #10593267 | C2 | semidirect |
| 8. C22×AGL(1,𝔽9) | C4 | semidirect |
| 14. C22⋊AGL(1,𝔽9) | C4 | semidirect |
| 35. C22⋊#157 | C8 | semidirect |
| 38. C32×C22⋊C4 | C8 | semidirect |
| 39. #3757 | C8 | semidirect |
| 40. #3752 | C8 | semidirect |
| 57. C2×#157 | C2×C8 | semidirect |
| 64. AGL(1,𝔽9) | C22⋊C4 | direct (N × H) |
| 65. C2×C32×C4 | C2×C8 | semidirect |
| 66. C2×C3⋊Dic3 | C2×C8 | semidirect |
| 80. C22×C32 | C4×C8 | semidirect |
| 86. C2×C3⋊D3 | C4×C8 | semidirect |
| 148. C22⋊C4 | AGL(1,𝔽9) | direct (N × H) |
| 165. C32 | C8×C22⋊C4 | semidirect |
| 188. C2×C4 | C2×AGL(1,𝔽9) | semidirect |
| 209. C22 | C4×AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×AGL(1,𝔽9) | 2 |
| C2×C22⋊AGL(1,𝔽9) | 2 |
| C2×C4×AGL(1,𝔽9) | 2 |
| C22⋊C4×#157 | 2 |
| #10593267 | 2 |
| C8×C22⋊C4 | 9 |