Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1446 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1446 conjugacy classes of subgroups — too many to draw. Only its 287 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 |
|---|---|---|
| 2. C23×AGL(1,𝔽9) | C2 | semidirect |
| 3. C2×C22⋊AGL(1,𝔽9) | C2 | direct (N × H) |
| 11. C22×AGL(1,𝔽9) | C22 | semidirect |
| 12. C22⋊AGL(1,𝔽9) | C22 | direct (N × H) |
| 13. C24×C32 | C8 | semidirect |
| 16. C23×C3⋊D3 | C8 | semidirect |
| 17. C23×C3⋊D3 | C8 | semidirect |
| 30. C2×AGL(1,𝔽9) | C23 | semidirect |
| 35. C23×C32 | C2×C8 | semidirect |
| 42. C22×C3⋊D3 | C2×C8 | semidirect |
| 43. C22×C3⋊D3 | C2×C8 | semidirect |
| 67. C22×C32 | C22⋊C8 | semidirect |
| 69. C22×C32 | C22×C8 | semidirect |
| 74. C2×C3⋊D3 | C22⋊C8 | semidirect |
| 77. C2×C3⋊D3 | C22×C8 | semidirect |
| 107. C2×C32 | C2×C22⋊C8 | semidirect |
| 110. C3⋊D3 | C2×C22⋊C8 | semidirect |
| 119. C24 | AGL(1,𝔽9) | semidirect |
| 145. C32 | C22×C22⋊C8 | semidirect |
| 159. C23 | C2×AGL(1,𝔽9) | semidirect |
| 187. C22 | C22⋊AGL(1,𝔽9) | direct (N × H) |
| 189. C22 | C22×AGL(1,𝔽9) | semidirect |
| 199. C2 | C2×C22⋊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 |
|---|---|
| C24×#157 | 2 |
| C23×AGL(1,𝔽9) | 2 |
| C2×C22⋊AGL(1,𝔽9) | 2 |
| C22×C22⋊C8 | 9 |