Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
334 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 100 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 | semidirect |
| 13. AGL(1,𝔽9)⋊C4 | C4 | direct (N × H) |
| 48. AGL(1,𝔽9) | C42 | semidirect |
| 76. C32×C4 | #106 | semidirect |
| 77. C3⋊Dic3 | #106 | semidirect |
| 131. C32 | C4×#106 | semidirect |
| 168. C4 | AGL(1,𝔽9)⋊C4 | 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×AGL(1,𝔽9)⋊C4 | 2 |
| C4×#3777 | 2 |
| C4×#3773 | 2 |
| #10593166 | 2 |
| C4×#106 | 9 |