Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
248 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 6. C3×Q8×C9 | C4 | semidirect |
| 20. C9×Dic3 | Q8 | direct (N × H) |
| 22. Q8×Dic3 | C9 | direct (N × H) |
| 28. Q8×C9 | Dic3 | direct (N × H) |
| 54. C3×C9 | C4×Q8 | semidirect |
| 56. C3×Q8 | C4×C9 | semidirect |
| 86. Dic3 | Q8×C9 | direct (N × H) |
| 89. C9 | Q8×Dic3 | direct (N × H) |
| 90. Q8 | C9×Dic3 | direct (N × H) |
| 108. C3 | C4×Q8×C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C9 | 2 |
| C9×C4⋊Dic3 | 2 |
| C4×C9×Dic3 | 2 |
| C3×Q8×Dic3 | 3 |
| C4×Q8×C9 | 3 |