Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
176 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 40 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. C22×Q32 | C9 | semidirect |
| 49. C22⋊C9 | Q32 | direct (N × H) |
| 60. Q32 | C22⋊C9 | direct (N × H) |
| 112. C22 | C9×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×C22⋊C9 | 2 |
| C16×C22⋊C9 | 2 |
| C22×C3×Q32 | 3 |
| C9×Q32 | 4 |