Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
165 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 165 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 8. C9×Q16 | C4 | semidirect |
| 44. Dic9 | Q16 | direct (N × H) |
| 63. Q16 | Dic9 | direct (N × H) |
| 77. C9 | C4×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×Q16 | 2 |
| Q8×Dic9 | 2 |
| #63395 | 2 |
| #63378 | 2 |
| C8×Dic9 | 2 |
| Dic3×Q16 | 3 |