Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
514 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×C22⋊AGL(1,𝔽9) | C2 | semidirect |
| 3. C2×C4⋊AGL(1,𝔽9) | C2 | semidirect |
| 4. C2×C4×AGL(1,𝔽9) | C2 | semidirect |
| 29. C2×AGL(1,𝔽9) | D4 | semidirect |
| 30. C2×C32×D4 | C8 | semidirect |
| 31. C2×#638 | C8 | semidirect |
| 34. C2×C4⋊(C3⋊D3) | C8 | semidirect |
| 97. C32×C4 | C22⋊C8 | semidirect |
| 98. C3⋊Dic3 | C22⋊C8 | semidirect |
| 137. C2×D4 | AGL(1,𝔽9) | semidirect |
| 169. C32 | #1954 | semidirect |
| 222. C4 | C22⋊AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#157 | 2 |
| C2×C22⋊AGL(1,𝔽9) | 2 |
| C2×C4⋊AGL(1,𝔽9) | 2 |
| C2×C4×AGL(1,𝔽9) | 2 |
| #1954 | 9 |