Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
230 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. D4×AGL(1,𝔽9) | C2 | semidirect |
| 3. D4⋊AGL(1,𝔽9) | C2 | semidirect |
| 4. #10593252 | C2 | semidirect |
| 5. #10593251 | C2 | semidirect |
| 26. C32×D8 | C8 | semidirect |
| 27. #3753 | C8 | semidirect |
| 28. #3745 | C8 | semidirect |
| 41. C32×D4 | C2×C8 | semidirect |
| 43. C4⋊(C3⋊D3) | C2×C8 | semidirect |
| 46. C32×C8 | C2×C8 | semidirect |
| 47. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 94. D8 | AGL(1,𝔽9) | semidirect |
| 111. C32 | #1580 | semidirect |
| 115. D4 | C2×AGL(1,𝔽9) | semidirect |
| 127. C8 | C2×AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×AGL(1,𝔽9) | 2 |
| D8×#157 | 2 |
| D4⋊AGL(1,𝔽9) | 2 |
| #10593252 | 2 |
| #10593251 | 2 |
| #1580 | 9 |