Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
203 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 203 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 16. Q8×Q16 | C9 | semidirect |
| 32. Q8⋊C9 | Q16 | direct (N × H) |
| 84. Q16 | Q8⋊C9 | direct (N × H) |
| 105. Q8 | C9×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Q8⋊C9 | 2 |
| C8×Q8⋊C9 | 2 |
| C3×Q8×Q16 | 3 |
| C2×C9×Q16 | 4 |