Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
229 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 229 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 5. Q8×Dic9 | C3 | semidirect |
| 6. Q8×3−1+2 | C4 | semidirect |
| 20. 3−1+2⋊C4 | Q8 | direct (N × H) |
| 28. Q8×C9 | C3×C4 | semidirect |
| 51. Dic9 | C3×Q8 | semidirect |
| 53. 3−1+2 | C4×Q8 | semidirect |
| 84. C9 | C3×C4×Q8 | semidirect |
| 85. Q8 | 3−1+2⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×3−1+2 | 2 |
| C4⋊(3−1+2⋊C4) | 2 |
| C4×3−1+2⋊C4 | 2 |
| C3×Q8×Dic3 | 3 |
| Q8×Dic9 | 3 |