Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
430 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 71 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. #10596484 | C2 | semidirect |
| 3. #10596484 | C2 | semidirect |
| 4. D4⋊AGL(1,𝔽9) | C2 | semidirect |
| 17. C4⋊AGL(1,𝔽9) | C22 | semidirect |
| 19. C4×AGL(1,𝔽9) | C22 | semidirect |
| 29. C2×C32×D4 | C8 | semidirect |
| 33. D4×C3⋊D3 | C8 | semidirect |
| 35. C2×C4⋊(C3⋊D3) | C8 | semidirect |
| 160. C2×D4 | AGL(1,𝔽9) | semidirect |
| 194. C32 | #1478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#157 | 2 |
| #10596484 | 2 |
| D4⋊AGL(1,𝔽9) | 2 |
| #1478 | 9 |