Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
201 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 201 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 29. C9×C16 | Q8 | semidirect |
| 45. Dic18 | C16 | direct (N × H) |
| 104. C16 | Dic18 | direct (N × H) |
| 112. C9 | Q8×C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Dic18 | 2 |
| C4×C9×C16 | 2 |
| Dic9⋊C16 | 2 |
| C16×Dic9 | 2 |
| C4⋊(C9⋊C16) | 2 |
| C16×Dic6 | 3 |