Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 26. C32×Q16 | C8 | semidirect |
| 27. #3756 | C8 | semidirect |
| 28. #3746 | C8 | semidirect |
| 38. AGL(1,𝔽9) | Q16 | direct (N × H) |
| 89. Q16 | AGL(1,𝔽9) | direct (N × H) |
| 105. C32 | C8×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×AGL(1,𝔽9) | 2 |
| Q16×#157 | 2 |
| Q8⋊AGL(1,𝔽9) | 2 |
| #10593253 | 2 |
| C8×AGL(1,𝔽9) | 2 |
| C8×Q16 | 9 |