Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
258 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #10593251 | C2 | semidirect |
| 5. C8×AGL(1,𝔽9) | C2 | semidirect |
| 25. #3792 | C8 | semidirect |
| 30. #3788 | C8 | semidirect |
| 32. C32×M16 | C8 | semidirect |
| 33. #3748 | C8 | semidirect |
| 34. #3743 | C8 | semidirect |
| 47. AGL(1,𝔽9) | M16 | direct (N × H) |
| 54. #622 | C2×C8 | semidirect |
| 55. C32×C8 | C2×C8 | semidirect |
| 56. C3⋊(C3⋊C8) | C2×C8 | semidirect |
| 113. M16 | AGL(1,𝔽9) | direct (N × H) |
| 133. C32 | C8×M16 | semidirect |
| 152. 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 |
|---|---|
| #10596484 | 2 |
| C2×C4×AGL(1,𝔽9) | 2 |
| M16×#157 | 2 |
| #10593251 | 2 |
| C8×AGL(1,𝔽9) | 2 |
| C8×M16 | 9 |